Question

4. The figure below consists of a square and 2 semicircles, with dimensions as shown. What is the outside perimeter, in centimeters, Show all work or explain how you found your answer. of the figure?

Answer 1

Answer:

41.13 centimeters (rounded to 2 decimal places)

Step-by-step explanation:

The perimeter is the sum of all sides of the figure.

This figure consists of two semicircular lines (right and left) and two lines (top and bottom). We add up all of them and find the perimeter of the figure.

Left:

Semicircle perimeter = half of circle perimeter (aka circumference)

Circumference = 2πr, where r is the radius (half of diameter)

The diameter of the circle is 8, so radius is 8/2 = 4

So the circumference is:

C = 2πr = 2π(4) = 8π

Semicircle perimeter is half of that, so, 8π/2 = 4π

Right:

This is exactly same semicircle as the left one, so its perimeter is also 4π

Top:

The top is a side with length 8

Bottom:

Same as top, so the length is 8

Total perimeter = 4π + 4π + 8 + 8 = 16 + 8π = 41.13 centimeters