Area of Irregular Quadrilaterals: SASSS

This MATHguide [www.mathguide.com/] video demonstrates how to calculate the area of an irregular quadrilateral given four sides and an angle (SASSS). The Law of Cosines, Heron's Formula and the sine formula for area of a triangle are demonstrated.

[@MATHguide]

See our lessons on areas of polygons: www.mathguide.com/lessons2/AreaPoly.html

[@dbc3745]

The way you explain the solutions are easily understood. I hope you make more videos like this. I can't understand my teacher. Thank you so much.

[@MATHguide]

Glad the video helped.

[@dtruque]

This reminded me of a similar formula to Heron's formula that can be applied only to cyclical quadrilaterals (those that can be inscribed in a circle). It's called Brahmagupta's formula : A = (s-a)(s-b)(s-c)(s-d), where s = semiperimeter and a,b,c,d are the known sides. Note that it wouldn't apply in this problem because this is an irregular quadrilateral, not a cyclical (in a cyclical quadrilateral, opposite angles sum up to 180 degrees).

[@karthickauto9169]

hi sir, i having the measurement of 4 side but i dont know the angle how can i find the angle

[@MATHguide]

One must have an angle.

[@dtruque]

If the quadrilateral is inscribed in a circle (i.e., cyclical quadrilateral), you can use Brahmagupta's Formula: A=(s-a)(s-b)(s-c)(s-d), where s=semiperimeter and a,b,c,d are the sides. Note that all triangles can be inscribed in a circle, so Brahmagupta's formula works for triangles if you assume the "fourth" side has length = 0, i.e., back to Heron's formula.

[@anubhavpandey6481]

is it possible to calculate the area of quadrilateral if only the sides are given and no angle is given and the sides are different..i find it difficult because different shapes are obtained so the area changes in each case..

[@MATHguide]

Anubhav Pandey I think you answered your own question. No, more information is needed.

[@anubhavpandey6481]

MATHguide thank u

[@mengueternalgemnwi9075]

Sorry sir, with only the unegual sides given without any angle is it possible to find the angle?

[@MATHguide]

Watch the video.

[@luvoncamane4146]

I have a triangle with sides 25, 21, and 3. It equates to meth error when I use the formula. What can I do?

[@MATHguide]

See "triangle inequality".

[@soumitramakar9247]

Thank you sir

[@isaacsamadder348]

How to calculate the diagonal of irregular rectangle?

[@MATHguide]

Skillfully use the law of sines and law of cosines.

[@four2033]

Please calculate for me im buying a land. The sides are AB=173, BC=110, CD=138, DA=102

[@louisa9007]

Is it possible to find the area if only 2 sides are given with no angles?

[@MATHguide]

No.

[@louisa9007]

MATHguide thanks. I realised i had to find the length scale factor of the shape inside the irregular quadrilateral. then square it to find the area scale factor and times it by the inner shape which gives me the bigger shapes area scale factor. Hope that made some sense lol

[@fidelperez9514]

How you do it if you dont have an angle?

[@MATHguide]

It would be impossible to find the area of a generic quadrilateral without knowing an angle.

[@hotrodroxie]

Wish I could find a sixth grade version of this video. If anybody knows of one, thanks in advance for directing me!!

[@MATHguide]

This is not a topic for sixth graders.

[@Ivan-yb1cf]

How to find the angle

[@guillermogorosin5485]

Can you solve the aboved problem without an angle given.. thks.

[@MATHguide]

No.

[@boogerking7411]

How to compute the other diagonal length?

[@MATHguide]

booger king We can do it if we know the angle between the 30 degree and 150 degree angles. To get them, we need to calculate the other angles in the diagram, which is no easy task.

[@amanb5598]

How to calculate if no angle is given

[@MATHguide]

That would be impossible.

[@amanb5598]

@@MATHguide it is possible

[@Muqaddasmalik]

very impressive explanation

[@MATHguide]

malik mahar Thank you!

[@RashedNizamsatu]

How can I measure when angle is unknown??

[@MATHguide]

Which angle are you referring to?

[@pareshpatil1597]

@@MATHguide 80 degree... if not given how to find area

[@MATHguide]

@@pareshpatil1597 Break up the figure into triangles and then find their areas.

[@gururajghewari620]

How to find irregular quadrilateral when only lengths of sides given and angle is not given

[@MATHguide]

That's impossible.

[@nitishilovemykolkatapathak4849]

I like it

[@earthgraduate726]

You're assuming that you have the angle and the diagonal length, while it's not realistic. In real world you probably do not have have the diagonal and there's no way to calculate that without having an angle .

[@rikoruavihengari4661]

What about with no angle given?

[@MATHguide]

What is given to you?

[@seetu1500]

@@MATHguide only four sides. Is there any calculator online that you can recommend.

[@gabfar4328]

What if you don't have an angle?

[@MATHguide]

Gabriel Fardell See Panday's comment and response.

[@gabfar4328]

MATHguide thx mate

[@thechosenone6496]

Only 352 likes how?!?

[@MATHguide]

Yes. It's criminal. 😉

[@mattlo9055]

G.O.A.T. talk.

[@MATHguide]

Thank you very much!

[@davids9538]

very clear!

[@MATHguide]

Jean Jeas Thank you.

[@mengueternalgemnwi9075]

Please is there a possibility of finding the angle if only the sides are given?

[@livefreeordie9931]

140x20x80 = 224,000 dont know where you came up with that bogus number of 1378.73. Check your math

[@MATHguide]

Look at the formula for area: A = 0.5(140)(20)sin(80 degrees) = 1378.731 [rounded to the thousandths place].

[@erangaki]

H