Question

1. find the perimeter of this figure. corners that look square are square. dimensions are in meters.
2. a base of the right prism is the scalene triangle shown. the height of the right prism is 15 in. find the volume of the right prism.

Explanation:

Problem 29

Step1: Calculate the circumference of the semicircle

The formula for the circumference of a full - circle is \(C = 2\pi r\). For a semicircle, \(C_{semicircle}=\pi r\). Given \(r=\frac{20}{2}=10\) m, \(C_{semicircle}=\pi\times10 = 10\pi\) m.

Step2: Calculate the sum of the straight - line segments

We have two sides of length \(30\) m and one side of length \(20\) m. The sum of these straight - line segments is \(30 + 30+20=80\) m.

Step3: Calculate the perimeter of the figure

The perimeter \(P\) of the figure is the sum of the length of the semicircle and the sum of the straight - line segments. So \(P = 10\pi+80\). Using \(\pi\approx3.14\), we get \(P=10\times3.14 + 80=31.4+80 = 111.4\) m.

Step1: Calculate the area of the base (triangle)

The formula for the area of a triangle is \(A=\frac{1}{2}\times base\times height\). Given \(base = 14\) in and \(height = 6\) in, \(A=\frac{1}{2}\times14\times6=42\) in².

Step2: Calculate the volume of the right - prism

The formula for the volume of a prism is \(V=A\times h\), where \(A\) is the area of the base and \(h\) is the height of the prism. Given \(A = 42\) in² and \(h = 15\) in, \(V=42\times15=630\) in³.

Answer:

\(111.4\) m

Problem 30