Question

1. (20) a base of the right prism 8 meters high is shown. find the volume of the right prism. all angles are right angles. dimensions are in meters.

the base figure has dimensions: 6, 7, 5, 12, 10. there is also a 3d model of the prism. another figure has a length of 20 (partially visible).

Explanation:

Step1: Calculate the area of the base

The base can be divided into two rectangles.
First rectangle: length \(l_1 = 10\)m, width \(w_1=5\)m. Area \(A_1=l_1\times w_1 = 10\times5=50\) \(m^{2}\).
Second rectangle: length \(l_2 = 6\)m, width \(w_2=(12 - 5)=7\)m. Area \(A_2=l_2\times w_2=6\times7 = 42\) \(m^{2}\).
Total area of the base \(A=A_1 + A_2=50+42=92\) \(m^{2}\).

Step2: Calculate the volume of the prism

The volume formula of a prism is \(V=A\times h\), where \(h = 8\)m (height of the prism).
\(V=92\times8\)
\(V = 736\) \(m^{3}\)

Answer:

\(736\) cubic meters