can you solve for the coloured area

[@plormfingaround9962]

I could be mistaken but I'm pretty sure the answer here is incorrect. The first step was right, use the Pythagorean theorem to find side P of the larger square, which when simplified is 24.18m. After that, you would just use 1/2 b x h for the area of the shaded triangle, as you have the base and height measurements from the two squares. 12m x 24.18m / 2 = 145.08m^2. If I made a mistake somewhere, please inform me.

[@MathandEngineering]

Good day sir, well you can use the formula ½b×h also, but to us that, you have to choose one of the sides as your base, than calculate the height, that is a line perpendicular to the base which touches the vertex opposite to the base, though in the case of a Right angled triangle, the two perpendicular sides, each can be taken as the base or the height. But the triangle from the Question is not a Right angled triangle, because we calculated angle y to be equal to 180° - x, angle x is also one of the angles of the other right triangle, in a Right angled triangle, apart of the right angle, none of the two other angles can be up to 90°, the two are less than 90°. They are complementary. So this shows that x is less than 90° and we found y = 180° - x if you subtract x which is less than 90° from 180°, definitely the answer will be greatery than 90°, there fore y is greater than 90° and hence we have to use the formula ½absinC. I don't know if my explanation is clear,.but please if maybe you didn't understand, just tell me and I'll re explain. Thanks