Question

1. 10 m. perimeter (terms of pi) perimeter (number)

Explanation:

Step1: Identify the components of the perimeter

The figure has a semi - circle and two straight - line segments. The radius of the semi - circle is \(r = 10\) m. The length of each straight - line segment is \(10\) m.

Step2: Calculate the length of the semi - circular arc

The formula for the circumference of a full circle is \(C = 2\pi r\). For a semi - circle, the length of the arc \(l=\pi r\). Substituting \(r = 10\) m, we get \(l=\pi\times10 = 10\pi\) m. But the semi - circle in the figure seems to be a three - quarter circle. The length of a three - quarter circle arc is \(l=\frac{3}{4}\times2\pi r\). Substituting \(r = 10\) m, we have \(l=\frac{3}{4}\times2\pi\times10=15\pi\) m.

Step3: Calculate the total length of the straight - line segments

There are two straight - line segments each of length \(10\) m, so the total length of the straight - line segments is \(2\times10=20\) m.

Step4: Calculate the perimeter in terms of \(\pi\)

The perimeter \(P\) of the figure is the sum of the length of the arc and the length of the straight - line segments. So \(P = 15\pi+20\) m.

Step5: Calculate the perimeter as a number

Substitute \(\pi\approx3.14\) into \(P = 15\pi+20\). Then \(P=15\times3.14 + 20=47.1+20=67.1\) m.

Answer:

Perimeter (terms of Pi): \(15\pi + 20\)
Perimeter (number): \(67.1\)