Six identical rectangles are placed inside a square with side 32 cm as shown. What is the area shaded in yellow?
Let the longer side of the small rectangle = x
Let the shorter side = y
For the width of the square we have that
x + ( x - y) + x + (x - y) = 32
4x - 2y = 32
2x - y = 16 ⇒ -2x + y = -16 (1)
For the height of the square we have that
y + x + y + x + y = 32
2x + 3y = 32 (2)
Add (1) and (2) and we have that
4y = 16
y = 4
And x = 10
We can decompose the yellow area into 2 rectangles
One has a width of (32 - x) and a height of (x+ y)
So...its area = (32 - 10) ( 10 + 4) = (22) (14) = 308
And the other rectangle has a width of (x - y) and a height of (x + y)
So.....its area = (10 - 4) ( 10 + 4) = (6)(14) = 84
So....the yellow area = 308 + 84 = 392 units^2