Question

this shape is made up of one - half - circle attached to an equilateral triangle with side lengths 17 inches. you can use 3.14 as an approximation for π. you can use your zearn calculator to help you solve. the perimeter of the shape is about inches.

Explanation:

Step1: Identify the components of the perimeter

The perimeter of the shape is composed of two - side lengths of the equilateral triangle and the arc - length of the semi - circle. Let the side length of the equilateral triangle be \(s\). Since the semi - circle is attached to the equilateral triangle, the diameter of the semi - circle is equal to the side length of the equilateral triangle.

Step2: Recall the formulas

The formula for the arc - length of a semi - circle is \(l=\frac{1}{2}\times\pi\times d\) (where \(d\) is the diameter), and the side length of the equilateral triangle is \(s = d\). The perimeter \(P\) of the shape is \(P = 2s+\frac{1}{2}\times\pi\times s\).

Step3: Substitute \(\pi = 3.14\)

Let's assume the side length \(s = 7\) inches. Then \(P=2\times7+\frac{1}{2}\times3.14\times7\).
First, calculate \(2\times7 = 14\).
Second, calculate \(\frac{1}{2}\times3.14\times7=1.57\times7 = 10.99\).

Step4: Calculate the perimeter

\(P=14 + 10.99=24.99\approx25\) inches.

Answer:

25