Question

What is the perimeter and area of the photo below? And please show me how you did it. I need it for a school math group, and I’m struggling. So please show work.

Answer 1

Answer:

Assuming the area is made up of a square and a semicircle.

Perimeter

The side length of the square = 18 ft

We can see 3 full side lengths plus one side length from which we need to subtract 12 ft (see attached diagram).

⇒ perimeter of the square = (3 x 18) + (18 - 12)

                                                          = 54 + 6

                                                          = 60 ft

Circumference of a circle = $\pi$d (where d is the diameter)

⇒ arc length of the semicircle = 1/2 circumference

                                                  = 1/2 · $\pi$ · 12

                                                  = 6$\pi$ ft

Total perimeter = 60 + 6$\pi$ = 78.8 ft (nearest tenth)

Area

Area of a square = s² (where s is the side length)

⇒ area of square = 18²

                             = 324 ft²

Diameter = 2r  ⇒  r = 1/2 diameter

Area of a circle = $\pi$r²  (where r is the radius)

⇒ area of the semicircle = 1/2 · $\pi$ · 6²

                                         = 18$\pi$ ft²

Total area = 324 + 18$\pi$ = 380.5 ft² (nearest tenth)