Find the surface area of pyramids with the following nets.

Question

ScanSolve AI Tutor · Accepted Answer

let's find the surface area of this pyramid.

The net shows a square base and four triangular faces.

Identify the dimensions from the net.
The square base has a side length of $s = 8 \text{ cm}$ .
Each triangular face has a base of $8 \text{ cm}$ (which is a side of the square) and a height (slant height of the pyramid's face) of $h_t = 8 \text{ cm}$ .
Calculate the area of the square base.
$A_{base} = s^2 = (8 \text{ cm})^2 = 64 \text{ cm}^2$
Calculate the area of one triangular face.
$A_{triangle} = \frac{1}{2} \times \text{base} \times \text{height}_t$ $A_{triangle} = \frac{1}{2} \times 8 \text{ cm} \times 8 \text{ cm}$ $A_{triangle} = \frac{1}{2} \times 64 \text{ cm}^2 = 32 \text{ cm}^2$
Calculate the total lateral surface area (area of the four triangular faces).
$A_{lateral} = 4 \times A_{triangle} = 4 \times 32 \text{ cm}^2 = 128 \text{ cm}^2$
Calculate the total surface area of the pyramid.
The total surface area is the sum of the base area and the lateral surface area.
$A_{total} = A_{base} + A_{lateral}$ $A_{total} = 64 \text{ cm}^2 + 128 \text{ cm}^2$ $A_{total} = 192 \text{ cm}^2$
The surface area of the pyramid is $192 \text{ cm}^2$ .

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