Question

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find the surface area of this triangular prism. be sure to incl

Explanation:

Step1: Calculate the area of the triangular bases

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

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

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

Step2: Calculate the area of the rectangular faces

There are three rectangular faces.

• For the rectangle with sides \(7\) yd and \(6\) yd: \(A_1=7\times6 = 42\space yd^{2}\)
• For the rectangle with sides \(7\) yd and \(8\) yd: \(A_2=7\times8=56\space yd^{2}\)
• For the rectangle with sides \(7\) yd and \(10\) yd: \(A_3=7\times10 = 70\space yd^{2}\)

The total area of the rectangular faces is \(A_{rectangles}=42 + 56+70=168\space yd^{2}\)

Step3: Calculate the total surface area

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

$$ A=A_{triangles}+A_{rectangles}=48 + 168=216\space yd^{2} $$

Answer:

\(216\space yd^{2}\)