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Answer to Q176:
Find the area of the entire square!
We can take the other side of the orange rectangle to be a.
That means the area of the orange rectangle is 2 x a = 2a.
But we were told all the areas are equal, so the entire square should be 5 x 2a = 10a.
We can also take the length of the yellow rectangle to be c. That means the total length of the entire square is 2 + c.
That means the length and width of the four rectangles (excluding the blue one) will be 2+c and a.
This means the area of those four rectangles will be (2+c) x a which will be equals to 4 x (2a), remember?
so,
(2+c) x a = 4 x (2a)
2a + ac = 8a
divide all through by a
2 + c = 8
c = 8 - 2
c = 6
We now know the total length of the left hand side is 2 + c = 2 + 6 = 8
And remember we were told the entire shape is a square, so the width of the entire square will also be 8.
Area of entire square = 8 x 8
= 64
Answer: 64 sq. unit
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