Question

Two semicircles are attached to the sides of a rectangle as shown.

Answer 1

answer:

157 inches²

step-by-step explanation:

• we have to break this down into parts and find the area of each part and then add them up so we have the area for the whole thing

rectangle:

5 X 14 = 70 inches²

big semicircle:

• solve this like a simple circle and then divide by 2 since this is half

area = πr²

• insert what we know from the question

area = (3.14)(7)²

• the radius would be seven because as you can see the length of a side of the rectangle is 14 and this is also the diameter of the circle since they are attached and share it
• the radius is half of the diameter so we get 7

area = 3.14(49)

        = 153.86 inches²

• now divide this by 2 since it is semicircle

153.86 / 2 = 76.93 inches²

small semicircle:

area = (3.14)(2.5)²

• i followed the same method as last, except the numbers are different

area = 3.14(6.25)

        = 19.625 inches²

• now divide by 2

19.625 / 2 = 9.8125 inches²

• finally, add up all the separate areas you got

70 inches² + 76.93 inches² + 9.8125 inches²

= 156.7425 inches²

= 157 inches²

Answer 2

Answer:

• 157 in²

Step-by-step explanation:

The area of the shape is the sum of three sections

1. Rectangle

• A = 5*14 = 70 in²

2. Bigger semicircle

• A = 1/2π(14/2)² = 76.96 ≈ 77 in² (rounded)

3. Smaller semicircle

• A = 1/2π(5/2)² = 9.8174 ≈ 10 in² (rounded)

Total area:

• 70 + 77 + 10 = 157 in²