Question

I'LL GIVE BRAINLIST TO THOSE WHO WILL ANSWER IT CORRECT. ​

Answer 1

Answer:

• 28 cm²

Step-by-step explanation:

• Refer to attached

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