Question

Does the sum of the areas of the smaller squares equal the area of the larger square?
A = (1 1/2) ^ 2 = 2 1/4
1 1/2
A = (2 1/2) ^ 2 = 6 1/4
2 1/2
No
Yes
2
A = 2 ^ 2 = 4

Answer 1

No.

Compute each area:
- (1 1/2)^2 = 1.5^2 = 2.25
- (2 1/2)^2 = 2.5^2 = 6.25
Sum = 2.25 + 6.25 = 8.5

The larger square shown has area 2^2 = 4, which is not 8.5. So the sum of the smaller squares' areas does not equal the larger square's area. (If you wanted a square with area 8.5 its side would be sqrt(8.5) ≈ 2.9155.)