Question

Find the surface area of a square pyramid with side length 6 m and slant height 7 m.
4ft, 4ft, 6ft

Answer 1

To find the surface area of a square pyramid, we need to calculate the area of the base and the area of the four triangular faces.

1. **Area of the Base**: The base of the square pyramid is a square.
\[
\text{Area of Base} = \text{side}^2 = 6 \, \text{m} \times 6 \, \text{m} = 36 \, \text{m}^2
\]

2. **Area of the Triangular Faces**: Each triangular face has a base equal to the side length of the square and a height equal to the slant height of the pyramid.

The area of one triangular face is calculated using the formula:
\[
\text{Area of Triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 6 \, \text{m} \times 7 \, \text{m} = 21 \, \text{m}^2
\]

Since there are four triangular faces, the total area of the triangular faces is:
\[
\text{Total Area of Triangular Faces} = 4 \times 21 \, \text{m}^2 = 84 \, \text{m}^2
\]

3. **Total Surface Area**: The total surface area of the pyramid is the area of the base plus the total area of the triangular faces.
\[
\text{Total Surface Area} = \text{Area of Base} + \text{Total Area of Triangular Faces}
\]
\[
\text{Total Surface Area} = 36 \, \text{m}^2 + 84 \, \text{m}^2 = 120 \, \text{m}^2
\]

Thus, the surface area of the square pyramid is **120 m²**.