Question

1. find the surface area of this right trian-(15) gular prism. dimensions are in feet.

Explanation:

Step1: Calculate the area of the triangular bases

The formula for the area of a triangle is \(A=\frac{1}{2}bh\). Here, \(b = 8\) and \(h=6\).

$$ A_{triangle}=\frac{1}{2}\times8\times6=24 $$

Since there are \(2\) triangular bases, \(A_{triangles}=2\times24 = 48\)

Step2: Calculate the area of the rectangular faces

There are three rectangular faces.

• For the face with sides \(15\) and \(8\): \(A_1=15\times8 = 120\)
• For the face with sides \(15\) and \(6\): \(A_2=15\times6=90\)
• For the face with sides \(15\) and \(10\): \(A_3=15\times10 = 150\)

Step3: Sum up all the areas

The surface area \(S\) of the prism is the sum of the areas of the triangular bases and the rectangular faces.

$$ S=48+120 + 90+150 $$

$$ S=408 $$

Answer:

\(408\) square feet