Question

solve it PLZZ if you can!!
I need proper solution with explanation.
don't post fooly answer if u can't solve. let others solve it.​

Answer 1

Answer:

        28 cm²

Step-by-step explanation:

Let d be half the side of the square.

Use coordinates with the bottom left corner at the origin (0,0) and the bottom side along the x-axis, so the corners are (0,0), (2d,0), (0,2d), (2d,2d).

Let the coordinates of the point inside the square be (x,y).

Drawing a line from the bottom left corner to (x,y), the bottom left region is divided into two triangles.  The area of one triangle is

• (base × height) / 2  =  dy/2

and the area of the other triangle is

• (base × height) / 2  =  dx/2

As the area of that region is 16, this gives

• dx/2 + dy/2 = 16   ⇒   dx + dy = 32      ...(1)

Similarly, drawing a line from the top left corner to (x,y) divides the top left region into two triangles.  One of these triangles has area dx/2, and the other triangle has area d(2d-y)/2, as its height is 2d-y.  Together, this gives

• dx/2 + d(2d-y)/2 = 20   ⇒   2d² + dx - dy = 40      ...(2)

Doing the same again for the top right corner gives

• 4d² - dx - dy = 64      ...(3)

Doing the same for the bottom right gives

• Area of bottom right region = (2d² - dx + dy)/2.

Taking (3) - (2) + (1) gives

    (4d² - dx - dy) - (2d² + dx - dy) + (dx + dy) = 64 - 40 + 32

⇒  2d² - dx + dy = 56

⇒  (2d² - dx + dy)/2 = 28

Therefore the area of the bottom right region is 28 cm².