Question

find the surface area of this triangular prism. be sure to include the correct unit in your answer. your answer

Explanation:

Step1: Calculate the area of the triangular bases

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

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

Since there are two triangular bases, \(A_{total - triangles}=2\times24 = 48\space in^{2}\)

Step2: Calculate the area of the rectangular faces

There are three rectangular faces.

• For the face with sides \(6\) in and \(10\) in: \(A_{1}=6\times10 = 60\space in^{2}\)
• For the face with sides \(8\) in and \(10\) in: \(A_{2}=8\times10=80\space in^{2}\)
• For the face with sides \(9\) in and \(10\) in: \(A_{3}=9\times10 = 90\space in^{2}\)

The total area of the rectangular faces is \(A_{total - rectangles}=60 + 80+90=230\space in^{2}\)

Step3: Calculate the total surface area

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

$$A=A_{total - triangles}+A_{total - rectangles}$$

$$A = 48+216$$

$$A=264\space in^{2}$$

Answer:

\(264\space in^{2}\)