A square is inscribed in a circle with radius = 4, what is the area of the square?

[@MrMousley]

Imagine cutting the square into four pieces through the corners. You now have four right angled triangles. Now put the four triangles together to make two squares. These squares are 4 x 4 ... so the total area is 2 (4 x 4) = 32

[@Something162]

This is so simple no formula or trig required, took a couple of minutes but that's what I came up with.

[@williamBryan-k2e]

I thought at first - Naw!. but now I see it - ingeneous

[@coupsdestylo]

What I did too.

[@michaelorians5762]

Elegant solution

[@patrickcorliss8878]

Exactly. Did it in my head very slightly differently. One right-angled triangle has sides 4 and 4. If this was expanded to a square the area would be 16. But being half of that square, the area of the triangle must be 8. As there are four of them the total is 4 times 8 or 32.

[@OldJoe212]

Too much work. The Area of a triangle = 1/2bh. We know the base is 8. The height is 4, therefore the area is 16. There are 2 triangles so, 2x16=32.

[@tripleg2513]

This works, but its better to know the dimensions in case you need to work with it again

[@davidsandrovitch7635]

Having seen this, it wouldn't surprise me if there wasn't a geometric solution where you can construct a square based on the circle radius, and show that is equal to 2 inscribed squares. On reflection clearly you get 4 large triangles in an 8x8 square, of the same size as our 2 so the area of 2 triangles is 1/2 x 8 squared, also 32. You could fold the large square into two equal smaller squares.

[@richardsanders3567]

Exactly my thoughts

[@Logical_Funda]

​@@davidboyle4798 how do you know height is 4 !

[@philipmumford7871]

disagree. his solution is easy and would be how I would do it in my head. 2x^2 = 64 so x^2= 32 then just specify square units depending on what was in the original question.

[@mickk8519]

Gosh, this is so simple. The formula to find the area of a square within a circle is just. Radius squared times two. And that is it, nothing more, and nothing less. And don't get confused with the way the formula for finding the area of a circle works. Because the diameter squared will double the required answer for finding the area of the square. 4×4=16 16×2=32 Whereas. 8×8=64

[@Anunknowncat2593]

So we know that diagonals of a square bisect each other and are equal , and we know that the diagonal of a square is =√2*side The radius of the circle is 4 so the diagonal of the square or the diameter of the circle is 8 . So , we can write that- side*√2 =8 Or, side =8/√2 So the area of the square is (8/√2)^2 Or, 64/2 Or, 32 cm^2. (ans)

[@stevedietrich8936]

The diagonal of the square is the same as the diameter of the circle, so we know that the diagonal of the square is 8. If the diagonal of the square is 8 then each side of the square is the square root of 32, so the area of the square is base times height or 32.

[@christopherstamp5384]

32??? R u sure it isn't 16 it has to be a square because squares sides are equal and nothing 32 is not anything squard

[@stevedietrich8936]

@@christopherstamp5384 Yes, I am sure it is 32. The line that goes corner to corner through the square represents the hypotenuse of a right triangle whose base and height are equal. The hypotenuse is 8 which we know because it is also the diameter of the circle. If the hypotenuse is 8, the Pythagorean theorem says the base squared plus the height squared is equal to the hypotenuse squared. The hypotenuse (8) squared is 64, so since the base and height are equal, the base squared (and the height squared as well) have to be 32, because 32 plus 32 equals 64. If the base squared is 32, then the base is the square root of 32. Now to find the area of the entire square you multiply the base (square root of 32) times the height (square root of 32). The square root of 32 times the square root of 32 is (voila) 32.

[@BobCavaliere-x1e]

Why the issue? The area of the triangle is half the base times the height of the triangle, the radius is 4 which is also the height of the Triangle, 2(half the height times 8 the base times 2 as there are 2 triangles equals 32 for the sq. Easy peezy why the long drawn out answer?

[@BenjamenMeyer]

r=4 There are 4 triangles that have 2 sides of length r. Therefore: A=(0.5*b*h)*4 (0.5*4)*4 -> (2*4)*4 -> 8*4 -> 32 Also, 2 triangles with a base of 8 and height of 4. Same result.

[@ZolarV]

You can bisect the square with a line with length D at a vertex. D=2r. The resulting triangle is a right triangle who's hypotenus is 2r. By pythag theorem 2r^2 = base^2 +height^2. And base = height r = base. So A =r^2 = 16.

[@peregreena9046]

The square circumscribing the circle has an area of d*d=8*8=64 square units. Now if you rotate one of the now two squares by 45 degrees, the corners of the small square touch the centre of the large square. According to some ancient greek, that's the way to cut the larger square in half. so the inner square has half the area of the large square ... 32 square units

[@juergenilse3259]

Really interesting solution. It seems to be the second solution without using pythagoras ... You don't need torotate the big square,if you construct it by adding the tangent lines to the circle with the corners of the small square as touching points.

[@adamglltt89]

Interesting solution.

[@atulrastogi4836]

All are correct though Pythagoras eq is the simplest. However, tutor is too much descriptive with unnecessary talk.

[@juergenilse3259]

I don't think, that the simplest solution uses pythagoras ... Add both diagonales to the square. Theses divide the square in 4 isosceles rectangular triangels. The lega of those rectangular triangles are each equal to the radius of the circle, so the area of each of the triangles is r^2/2=16/2=8. The area of the square is the sum of the area of those triangles i.e. 4*8=32.

[@iangraham871]

So there is a standard formula for the area of an inscribed square which is one-half of (d squared), right? That is quite useful! Thanks

[@TheAZZA0990]

Really straightforward!! Shaded square A = 4x 4/2 x 4 = 32 sq. units!!! :)

[@adamglltt89]

I got 32 by using Pythagoras theorem.. because we know the length of the diagonal between two corners is twice the radius. However having read the comments, knowing this figure its far easier to just work out the area of the two triangles you've made when you cut square diagonally.

[@topkatz58]

Since the diagonal of the square is the same as the diameter of the circle. Diam of circle = 2 X Radius of the circle = 2 X 4 = 8 Call one side of square = a Area of square = a² By pythagorean theorem 2a² = 8² a² = 64/2 = 32 = Area of Square

[@thomassicard3733]

Pythagorus!!!! What DAWWWWG he was, eh?

[@ankammarao1002]

Radius = 4 units. Diameter = 8 units. Diameter = Diagonal of square ( diagonal of Square= root 2 x side of Square ). side of Square = 4x root 2. Area of Square = 32 Sq units.

[@d-tj1928]

A²+B²= C². 2 sides of triangle gives you the hypotenuse which is also diameter (D)... π(d/2)² = area

[@kennethwright870]

R=4, so d=8, The square is also two identical triangles, each with a base = d = 8 and height of r=4. So area of square = base * height, or 8*4 = 32.

[@roland3et]

Area of a square: A=½d² d: diagonal Therefore A=½*8²=64:2=32 It's as simple as that. 🙂👻

[@panlomito]

I love these puzzles... the centre of the circle is also the centre of the square. So the diagonal of the square is equal to the radius of the circle (4). Now we have a triangle (45-90-45°) that we can calculate (Pythagoras): 4² + 4² = s² with s is the length of a side of the square. So s² = 32. And the area of the square is s x s = s² so the area is 32 units.

[@darkparker7500]

8 * 8 = 64 = hypotenuse 8² = a² + b² 2 equal sides left to calculate 64/2 = 32 √32 = 5.567 8² = 5.657² + 5.567² Area of square = Length * Width 5.657 * 5.657 = 32² Area of square = 32²

[@athar_adv]

Using trigonometry: We know the diagonal (aka hypotenuse of a right triangle inside the square) is length 8, and the angle is 45°, so to find one of the sides of the square we just do 8sin(45°) wich is 4sqrt(2), and since the area of a square is a² where a is the length of the sides, since theyre all the same just plug in 4sqrt(2) into a² and you get 32. Ez

[@martinkabat1177]

Not sure if someone said it here. In my view the simplest solution and use of geometry knowledge is to use radius, to build diagonals in the square. You get 4 identical triangles. 2 triangles make square with are of 16 square units. 4 triangles make 2 squares 2x 16square units.

[@argonwheatbelly637]

32 sq units. 3 seconds. The area of an inscribed square is equal to 2r².

[@christopherstamp5384]

Nope.. a square can't be 8units by 4 units that's a rectangle... U calculated the area of 2square

[@XarraXonna]

Great video, but why make it so complicated? I did it in a few seconds in my head. Extend from the center to the 4 corners amd cut the square there. You have 4 isosceles right triangles with a short side of 4. The four of these make 2 squares with a side length of 4. 4x4=16 There are two of these squares, so 16x2=32sq units.

[@matthewyounger6834]

The triangle of a square is a 45-45-90 triangle. The legs are sqrt2/2 the radius. Area of the square is (r*sqrt2/2)^2. This seems the most intuitive answer to me...

[@BrendanAus]

Divide square into 4x right angle triangles all with a and b = r. (4 and 4 = 4^2 = 16). r^2 is the square made from a * b. (4 x 4 = 16). Area of a triangle in a polygon w * h = w * h / 2. Easy as a sqaure. a * b / 2 (4 * 4 = 16 / 2 = 8). There are 4 of them. 8 * 4 = 16. Didn't have to go to radicals or Pythagoras (though of course equally as valid).

[@incaroads001]

What about 8 * sin(45) = x, and then x^2 ?

[@DavidGrimberg]

One side (x) of the square is the hypotenuse of a right angle triangle whose legs are length r (the radius of the circle in which the square is inscribed) then by the Pythagorean theorem x2=r^2+r^2 simplified to x^2=2(r^2). So the area x^2 is 2(r^2). Plugging in the known value for r of 4 and solving for area 2(4^2) = 2(16) = 32

[@austinspencer8830]

As many people have noticed, the radius of the circle is also one-half the length of the line that divides the square into two isosceles right triangles. Because the legs of the triangles are of equal length, and a² + b² = c², the equation can be expressed as 2x² = 64, and x² = 32. √32, therefore, is the length of each side of the square, and 32 is its area.

[@goodyhi6989]

The length of each side of the square is √32, but the area is not the sum but the product: √32 × √32 = 32.

[@austinspencer8830]

@@goodyhi6989 Correct. Answer edited accordingly.

[@davidgodfrey3322]

One side of the small triangle is 4^2 +4^2 = 32, sqrt(32) is the length of one side so sqrt(32)^2 is 32 the area. You can do it in your head just looking at it. This is a simple method.

[@richardmelville5973]

Given that the area of a square, when given the diagonal is (D^2)/2 maybe the area of the square is 32 in whatever units are appropriate.

[@aym9638]

I have a request to make. Please sometimes check our comments and help us with the solutions of maths we need. Thanks for ur service ❤

[@StephenRayWesley]

A=LWH

[@StephenRayWesley]

a^2 b^2 c^2 =

[@panlomito]

​@@StephenRayWesley More likely the equation is a² + b² = c²

[@StephenRayWesley]

@@panlomito yes I agree

[@id0069]

If you draw 2 diags thru the square then you have a right angle triangle where the side of the square is the hypotenuse so its just Pythagorean theorem

[@beatasiepka8517]

agree, the simplest way

[@overseastom]

I got 32 units². To get the answer we eventually need to know the length of the square's side first, and then to find the area of the square we just multiply it by itself (i.e., square it). We know the radius of the circle is 4 units, and if we draw a line of that length to 2 of the square's adjacent corners, it makes a right triangle, and allows us to figure out the length of the hypotenuse (which is also the length of the square's side). To do that we use the equation A²+B²=C², and when we plug in the side lengths we get 4²+4²=32 units². If we wanted to know the length of the side we'd calculate √32 and get 5.657ish, but since we actually need the square of that number anyway to get the area of the square, we can just leave it at 32 units².

[@DavidHeffron78]

Even easier. It's a diamond with width a d height 8. 8*8/2

[@kevinreist7718]

Yeah, but each of the 4 outside crescents is one forth of the difference between the circle's area and the square's area or 4.5664 square units (inches?). In case anyone was wondering.

[@squizza28]

Simple. Let a side of the square be y. Then 8² = 2y². 64 = 2y² Y² = 32 so that's the area.

[@juergenilse3259]

The circle has radius 4,so it's diameter is 8. The diagonal of the square is equal to the diameter of the circle, so it's equal to 8. The diagonal divides the square in 2 rectangular isosceles triangles. Accoriding to pythagoras, the square over one leg of this triangle is half of the square over the hypotenuse of this triangle. The square over one leg of this triangle is identical of the square in the circle and the square over the hypotenus is the square of the diameter of the circle i.e. 8^2=64. So the area of the square is 64/2=32. Another solution: Add the 2 diagonals to the square. These divide the square in 4 rectangular isosceles triangles with the radius of the circle as lengthof the legs. The area of each triangle is half of the product of it's legs i.e. r^2/2=16/2=8. The aea of the square is the sum of the areas of those 4 triangles=4*8=32. This solution does not need pythagoras ...

[@larrydickenson8922]

D squared equals 2A. Next problem.

[@TheRoydyboy]

V simple radius 4. Apply Pythagoras theorem if you project the radius from the centre to each vertex of the square you get a right angled triangle with the chord joining any two corners as the hypotenuse 😅. Sum of the square on the hypotenuse is sum of the square on the other two sides . 4x4= 16 Add 16 twice i.e. the squares on two sides and you get 32. The sq on the hypotenuse is therefore 32. Now you want area which is lxb and l=b in a square . Therefore area is sq root 32 x sq root 32= 32 Therefore the area is 32 sq whatever unit u use inches, cm, miles, km or whatever the size of your circle is 😂 So simple

[@kenschmidt6522]

Exactly how I approached the problem.

[@davidpereira9238]

Same here

[@bobgregory5713]

Radius is 4, diam = 8. Area of triangle 2x² = 64 Area of the square = x² X² = 32 Doh

[@Funny._Videos_95-p]

The other way You could calculate the Area of this square is by taking a formula where the diagonal line is d (in this case d is also equals to 2r) and the formula is d = a x sqrt(2). Now our d is 2(4)= 8, so d = 8. Now we're gonna plug in 8 for the d and we get, a x sqrt(2) = 8, divide both sides by sqrt(2), you get a = 8/sqrt(2). Now the area of a square is a2. So in our case square root is gonna cancel out with the exponent and what we'll have is A = 64/2 = 32 units ' 2. Your answer is still working but here;s how I got it :)

[@tomtke7351]

the diagonal of the square d = 2r (eq.1) by inspection square => equal length sides triangle inside square using the diagonal offers via pythagorean theorm that the diagonal is d = sqrt(s^2+s^2) = sqrt(2s^2) = s(sqrt(2)) (eq.2) given r = 4 (eq.1) d = 2r = 2(4) = 8 (eq.2) d = s(sqrt(2)) from above d = 8 8 = s(sqrt(2)) s = 8/(sqrt(2)) AREA of square is A = s^2 (eq.3) employing s from above: A = [8/(sqrt(2))]^2 = 64/2 = 32 sq-inches V E R I F Y: The square's corners inside the circle imply a pie cut into 4 sections. The angle between the pie cutting lines is 90°. (note circle = 360° of four identical angles of 90°. So an isosceles triangle from both circle's and square's center has sides = 4 Area of right triangle = (1/2)(W×H) W = H = 4 (1/2) (4×4) = 8 4 such triangles = 32 in^2 32 =❤ 32 in^2

[@welcometochiles6156]

I did something real goofy. 45⁰ in unit circle is √(2) / 2 both x and y. Multiply that by 4 (radius) for 2√2. That's half of one side, multiply by 2 for 4√2 (or √32). That's each side length. Square it for a total of 32.

[@matthewyounger6834]

I thought that was the most direct way to think about it, also.

[@williamBryan-k2e]

I used sin to get the side x - sine = opp/hyp - sine( 45) = x/8 = so x=8 * sine(45) = 5.6... square that answer = 82

[@jerry2357]

Before watching: Insert diagonal lines from each corner, splitting the square into four isosceles right-angled triangles. Each of these has two sides of length equal to the radius, i.e. 4. The hypotenuse is the side of the square. Now using Pythagoras, the square on the hypotenuse is equal to the sum of the squares on the other two sides. But the square on the hypotenuse is congruent with the square we are interested in, i.e. it has the same area. Think about it being reflected about the hypotenuse. So the area of the square is 4^2+4^2=16+16=32 square units.

[@juergenilse3259]

If you already have split the square in the 4 triangles, you don't need to calculate the side of the square toget the area of the square. You may just add the areas of the 4 triangles, that have each the area r^2/2 (the legs of each have length r). So you end up with 4*r^2/2=2*r^2=2*4^2=2*16=32 (calculated without using pythagoras).

[@jerry2357]

@@juergenilse3259 I prefer my method.

[@juergenilse3259]

@@jerry2357 it's up to you, but if i would use pythagoras.,i would prefer the method as in the video: diameter^2=2*area of the square

[@TheScriptPunk]

You have triangular quadrants of 4 unit legs and a hypotenuse If you multiply the radius times itself, you get a whole square area, but utilize only half. The half contained in the inscribed square is 4x4/2. So we get 8. Then, we do this 4 times, so 8x4. So 4r^2 / 2. Or 2r^2

[@patrickcorliss8878]

Exactly what I did. In my head in less than a minute.

[@uweskanal42]

Das kann man viel einfacher lösen. Man zeichnet in das Quadrat die Diagonalen ein. Und erhält 4 rechtwinklige Dreiecke mit einer Kathetenlänge von jeweils dem Radius. Diese kann man dann (in Gedanken) zu zwei Quadraten mit der Kantenlänge=Radius zusammen setzen. 4*4*2 = 32

[@john_mckinney]

Side of square is square root 32 (Pythagoras). Area is therefore 32.

[@CelineMcHugh]

X is length of side. So area = x squared. Diameter =8. Use Pythagoras and 2x squared = 64 X squared = 32....

[@fixmycomp]

Pythagoras theorum. Solve for the hypotunues and square it.

[@robertnabholz2062]

2x(side of square squared) = diameter of circle squared.

[@rickperez8044]

Wait. A square is a special case of a rhombus: So, Area = Length of Diagonal^2/2. Right?

[@shappp1]

I did (8•sin(45))^2 (exact value of sin(45) is 1/√2)

[@adifox6877]

What class is this exercise for?

[@urrywest]

What would be interesting is a description of how many ways you can solve this.... I am sure there are at least ten.

[@dr.lareme7737]

(cos 45 x 8) ^2

[@advancedautomotivemachine4791]

I just split it into 2 triangles. 1/2 x b x h 1/2x8x4 =16 Times 2 =32

[@Surreal_Wizard]

I have no idea how to solve this or where to start, but I used a tape measure and came up with thirty two square farburglotts.

[@kenschmidt6522]

There are four right triangles, legs all equal radius of 4. 4 squared + 4 squared = 32

[@raya.pawley3563]

Thank you

[@bobcarn]

I'm going to go out on a limb and say.... 32? The long edge of the square should be able to be calculated by the pythagorean theorum (adding the square of each side of the right angle will yield the square of the hypotenuse... a^2 + b^2 = c^2). If the circle has a radius of 4, then each of the shorter sides of the triangle will be 4. So 4^2 is 16. 16+16=32. The long side is the square root of 32. But the square root of 32 times the square root of 32 is 32. It works out in my head, but I'm not sure if that's really teh way to figure it out. Now to find out. ... Yay!!!

[@st.george007]

4 x 0.5 x 4 x 4 = 32 or 4 x 1/2bh where b=4 and h=4.

[@rayjil7435]

1/2 base times Height (2)=32

[@davidsandrovitch7635]

I thought you have 4 right angled triangles with sides 4, so the hypotenuse is sqr root of 2x 4 squared. So the hypotenuse is root 32, and the area of the whole square is therefore 32. I like the other insight of just taking 2 large triangles, as you never even have to consider the potential complications of square roots

[@juergenilse3259]

If you look at the 4 small triangles, why do you calculate their hypotenuse instead of just adding their areas to get the area of the square? The area of each of the triangles is half of the product of it's legs: r^2/2=4^2/2=16/2=8. So the area of the square is 4*8=32. You don't need to calculate the length of the sides of the square to get it's area.

[@davidsandrovitch7635]

@@juergenilse3259 because at time I did it, I was thinking of using Pythagoras on 4 right angled triangles, not directly calculating the area of 2 larger triangles. I should say I was doing this quickly in my head, as most of the commentators are, I imagine.

[@devonwilson5776]

Greetings. The answer is 32 square units. Let us assume that the side of the square is X units. Now, based on the details given we know that the diagonal of the square is 8 units and the square is made up of two isosceles triangles. Using either of the triangles, and knowing that the base of the triangles is the diagonal of the square. Further, the base angles are 45 degrees. We can now solve for X. Sin 45 =X/8 units, and X= 8 times Sin 45 =8×.7071=5.6569 units. Now, to find the area of the square, we will use A= sides squared. That is 5.6569^2 square units =32 square units. Lovely.

[@thomassicard3733]

Or just consider both triangles are indeed RIGHT triangles and use a^2 + b^2 = 64. Pythagoras comes in handy.

[@devonwilson5776]

@@thomassicard3733 Greetings. Blessings.

[@johnspencer9217]

XSQ +XSQ= 8SQ 2XSQ =64 as in 8x8=64 /2 = 32

[@trevcam6892]

I did it this way using Pythagoras. The diagonal (hypotenuse) is 8. 8^2 = 64. If the sides are S, then S^2 + S^2 = 64. The area is S^2 = 64÷2, 32. I did it in my head because I'm sitting in my easy chair and can't be bothered to get up to fetch pencil and paper. It was the first solution to enter my head, although there are clearly other ways. I think this is the simplest and quickest.

[@davidboyle4798]

I have found a different way. 1/8 x 4= 0.5 x 4= 2 x 16= 32 in^2 4^2=16

[@StephenRayWesley]

a^2 b^2 c^2

[@stevewaters449]

Far, far, to much talking 🤦🏼

[@danieldennis9831]

Radius is 4 the square has corner to corner of 8 2s^2=64 s^2=32 which is the area.

[@marybrewer739]

I love your show, but it is sad that I am so poor at math! 😥😵‍💫

[@StephenRayWesley]

You can do it A=LWH

[@StephenRayWesley]

a^2 +b^2 c^2 =

[@mmmcleod2003]

So what was the answer?

[@thomassicard3733]

Totally easy as a Pythagorus deal.

[@juergenilse3259]

Pythagoras is not necessary, if you add the 2 diagonals to the square, which divide the square in 4 equal rectangular isosceles triangles. The area of each of those triangles is half of the product of it's legs, but the legs are each the same as the radius of the circle (the intercept of the diagonals is the center of the circle). So each of the triangles has area r^2/2=16/2=8 and the area of the square is 4*8=32.

[@shaveraaron]

"off on tangents” guys got geometry jokes

[@anthonybessinger2652]

Basic Pythagorean theorem

[@scottevans904]

Why am i coming out with 32.0356 for the area if u brake it down and give x a value of 5.66?

[@greenmanofkent]

Because 5.66 is not an exact value - it is only a 2-decimal rounded approximation of sqr(2)*4. However, even though sqr(2) is irrational, we know then that sqr(2)*sqr(2) = 2 (exactly), so when you square 4*sqr(2), you get an exact answer of 32.

[@bareegofast]

You explained not the hard way. So this is what I can up with. Radius= 4cm Diameter= 2(radius) = 8cm. Now if you look at the figure you can see that you can draw a diagonal which is equal to the diameter of the circle. (In this case that diagonal acts as both diagonal and the diameter of the circle). So as the diameter is=8cm So diagonal=8cm Now we know that all sides of a square are same and so is the diagonal so. Area of square= 8x8= 32. Easy.

[@johnmccaffrey5942]

Er 8x8 is 64

[@jebbiekanfer8843]

a sq+ b sq = rx2

[@flamespear86]

Too much rambling. People don't need gold stars they just need the knowledge.

[@Nikioko]

(4√2)² = 32. Took 3 seconds. He talks about it for 13 minutes.

[@MommaBird52]

If you had asked for perimeter we would have solved x.

[@sdrtech]

Radius x2 x 1.41 easy way

[@jebbiekanfer8843]

=(2xr) sq

[@pavillokteff185]

Or you could just go 4(square root of, two)(4)(square root of, two)

[@markcrites7060]

13 and 1/2 minutes to come up with something I can do in my head in less than a minute.

[@tobingj]

You're a genius. Work at NASA? Aimed at 12-14 year olds - explained well.

[@markcrites7060]

@@tobingj perhaps the title should explain that. I have a lot of math videos come across my feed. None of them are this simplistic. Just a retired mechanical engineer here who likes to keep a little bit in the action.

[@harrymatabal8448]

Markus you used your head but this guy used his ass from Bodmas

[@harrymatabal8448]

​@@tobingjwell said

[@russelllomando8460]

woo hoo, got it. thanks.

[@thomaszaccone3960]

Use pythagorean theorem

[@MarkWilliamNorth]

R times R times 2

[@margritkaminsky1470]

32

[@KarenWebb-q4j]

16

[@StephenRayWesley]

A=LWH

[@deograciousuwiragiye8429]

Area of a square is 2x2= 4.

[@DavidHeffron78]

Too complicated, folks. Its a diamond with height and width 8. 8*8/2

[@stephengabb2742]

32 units squared❤

[@doreenleeming4630]

64

[@bikerrick]

Why in the world did you go through all that rigamarole

[@harrymatabal8448]

Ok 32

[@charlesstarling1091]

16 oops times 2

[@nickcook2714]

Anyone who needs this problem explained in this much intricate detail will probably get lost because they won't understand what you mean when you say "we can now solve for", instead of "we can now work out". Also I've heard of pythagoras' theorem, or even the pythagorean theorem, but I'm not sure what the Pythagoram theorem is. There's also another interesting relationship with squares and circles which is, the area of a square inscribed touching the outside of a circle is twice the area of a square inscribed touching the inside of a circle.