Question

A net of a rectangular pyramid is shown in the figure. What is the surface area of the pyramid?

97.25in
131.5in
194.5in
257.5in

Answer 1

C) 194.5 in²

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Explanation:

The given net of the rectangular pyramid is made up of:

• One rectangle (width = 7 in, length = 9 in).
• Two congruent triangles (base = 7 in, height = 8.5 in).
• Two congruent triangles (base = 9 in, height 8 in).

The area of a rectangle is the product of its width and length.

The area of a triangle is half the product of its base and height.

To calculate the total surface area of the pyramid, sum the areas of the rectangle and triangles.

`\begin{aligned}\textsf{Total S.A.}&=\sf Area_(rectangle)+2\cdot Area_(Triangle\;1)+2 \cdot Area_(Triangle\;2)\\\\&=(7 \cdot 9)+2\left((1)/(2) \cdot 7 \cdot 8.5\right)+2\left((1)/(2) \cdot 9 \cdot 8\right)\\\\&=63+2\left(29.75\right)+2\left(36\right)\\\\&=63+59.5+72\\\\&=194.5\; \rm in^2\end{aligned}`

Therefore, the total surface area of the pyramid is 194.5 in².