Question

The net of an isosceles triangular prism is shown. What is the surface area, in square units, of the triangular prism?

Answer 1

Here, the surface area, in square units, of the triangular prism is 152 units².

We know that the area of any triangle can be calculated as

Area = 1/2 * base * height

The area of any rectangular figure can be calculated as

Area = length * width

Here, the length of the rectangular portion of the prism is 8 units.

The width of the lowermost rectangle is 5 units.

The area of the uppermost rectangle = the area of the lowermost rectangle = 8 * 5 units² = 40 units²

Again the width of the middle rectangle is 6 units.

So, the area of the middle rectangle = 6 * 8 units² = 48 units²

Now, the height and base of the triangles are 4 and 6 respectively.

So, the area of the left-hand side triangle = the area of the right-hand side triangle = 2 * (1/2) * 4 * (6/2) units² = 1 * 4 * 3 units² = 12 units²

Then the area of the triangular prism = area of rectangular portion + area of triangular portion = (2 * 40 + 48) + (2 * 12) units² = (80 + 48) + 24 units² = 128 + 24 units² = 152 units²

Therefore the surface area, in square units, of the triangular prism is 152 units². So, Option C is correct.

Learn more about the area here -

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