Question

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

Explanation:

Step1: Calculate the area of the triangular bases

The formula for the area of a triangle is \(A=\frac{1}{2}bh\). Here, \(b = 10\space m\) and \(h=24\space m\).

$$ A_{triangle}=\frac{1}{2}\times10\times24 = 120\space m^{2} $$

Since there are two triangular bases, \(A_{triangles}=2\times120 = 240\space m^{2}\)

Step2: Calculate the area of the rectangular faces

There are three rectangular faces.

• For the face with sides \(10\space m\) and \(11\space m\): \(A_{1}=10\times11 = 110\space m^{2}\)
• For the face with sides \(24\space m\) and \(11\space m\): \(A_{2}=24\times11=264\space m^{2}\)
• For the face with sides \(26\space m\) and \(11\space m\): \(A_{3}=26\times11 = 286\space m^{2}\)

The sum of the areas of the rectangular faces is \(A_{rectangles}=110 + 264+286=660\space m^{2}\)

Step3: Calculate the total surface area

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

$$ A=A_{triangles}+A_{rectangles}=240 + 660=900\space m^{2} $$

Answer:

\(900\space m^{2}\)