Answer:
Step-by-step explanation:
Let the half/side of the square be a and the difference of the point in the middle be x and y respectively
Each shape is the sum of 2 triangles, which have a base of a
The area to be found is A
We will show the area of each four shapes as:
- a(a-x) + a(a-y) = 16*2 ⇒ (1)
- a(a-x) + a(a+y) = 20*2 ⇒ (2)
- a(a+y) + a(a+x) = 32*2 ⇒ (3)
- a(a-y) + a(a+x) = A*2 ⇒ (4)
Now comparing the expressions:
- (2) – (1) = a(a + y -a + y) = 2ay = 8 ⇒ ay = 4
- (3) – (2) = a(a + x - a + x ) = 2ax = 24 ⇒ ax = 12
- (1) + (3) ⇒ 4a² = 96 ⇒ a² = 24
Using the values we got, finding the area A:
- (4) ⇒ 2A = 2a^2 - ay + ax = 48 - 4 + 12 = 56
- A = 56/2 = 28 cm²
