Question

1. find the surface area: 4 cm. 5 cm. 8 cm. 3 cm.

Explanation:

Step1: Calculate the area of the triangular bases

The formula for the area of a triangle is \(A=\frac{1}{2}bh\). Here, \(b = 3\space cm\) and \(h=4\space cm\).

$$ A_{triangle}=\frac{1}{2}\times3\times4=6\space cm^{2} $$

Since there are \(2\) triangular bases, \(A_{triangles - total}=2\times6 = 12\space cm^{2}\)

Step2: Calculate the area of the rectangular faces

There are three rectangular faces.

• For the rectangle with sides \(3\space cm\) and \(8\space cm\): \(A_{1}=3\times8 = 24\space cm^{2}\)
• For the rectangle with sides \(4\space cm\) and \(8\space cm\): \(A_{2}=4\times8=32\space cm^{2}\)
• For the rectangle with sides \(5\space cm\) and \(8\space cm\): \(A_{3}=5\times8 = 40\space cm^{2}\)

The total area of the rectangular faces is \(A_{rectangles - total}=24 + 32+40=96\space cm^{2}\)

Step3: Calculate the total surface area

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

$$ SA=A_{triangles - total}+A_{rectangles - total}=12 + 96=108\space cm^{2} $$

Answer:

\(108\space cm^{2}\)