Question

the curved edges of the shape formed by the solid black lines are half - circles. what are the area and perimeter of the shape? 16 cm 38 cm 38 cm 16 cm

Explanation:

Step1: Calculate the perimeter

The two semi - circles together form a full circle. The diameter of the circle is \(d = 16\) cm. The formula for the circumference of a circle is \(C=\pi d\). The straight - line parts of the perimeter are two lengths of \(38\) cm.
The circumference of the circle \(C=\pi\times16 = 16\pi\) cm. The total length of the straight - line parts is \(2\times38=76\) cm.
The perimeter \(P = 16\pi+76\). Taking \(\pi\approx3.14\), we have \(P=16\times3.14 + 76=50.24+76 = 126.24\) cm.

Step2: Calculate the area

The area of the two semi - circles together is the area of a full circle with radius \(r=\frac{16}{2}=8\) cm. The formula for the area of a circle is \(A=\pi r^{2}\). The area of the rectangle part is \(A_{rect}=38\times16\) cm².
The area of the circle \(A_{circle}=\pi\times8^{2}=64\pi\) cm². The area of the rectangle \(A_{rect}=38\times16 = 608\) cm².
The total area \(A=64\pi + 608\). Taking \(\pi\approx3.14\), we get \(A=64\times3.14+608=200.96 + 608=808.96\) cm².

Answer:

Perimeter: \(126.24\) cm, Area: \(808.96\) cm²