Question

5c) what are the area and perimeter of this shape? 6) if this equiangular shape was changed to a concave polygon with the same side lengths, would its perimeter increase, decrease, or stay the same? why?

Explanation:

Step1: Calculate the perimeter of the shape

The shape consists of two semi - circles (which together form a full circle) and two straight sides. The diameter of the semi - circles is 2 inches. The formula for the circumference of a circle is $C = \pi d$, and the length of each straight side is 2 inches.
The circumference of the circle formed by the two semi - circles: $C=\pi\times2 = 2\pi$ inches. The total length of the two straight sides is $2\times2=4$ inches. So the perimeter $P = 2\pi+4\approx2\times3.14 + 4=6.28 + 4=10.28$ inches.

Step2: Calculate the area of the shape

The area of the shape is the sum of the area of the square and the area of the circle formed by the two semi - circles. The area of a square with side length $s = 2$ inches is $A_{square}=s^{2}=2^{2}=4$ square inches. The area of a circle with diameter $d = 2$ inches (radius $r = 1$ inch) is $A_{circle}=\pi r^{2}=\pi\times1^{2}=\pi\approx3.14$ square inches. So the area $A=4+\pi\approx4 + 3.14=7.14$ square inches.

Answer:

Perimeter: $2\pi + 4\approx10.28$ inches
Area: $4+\pi\approx7.14$ square inches