Question

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

Answer 1

To find the surface area of a square pyramid, you can use the following formula:

\[
\text{Surface Area} = \text{Base Area} + \text{Lateral Area}
\]

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

2. **Calculate the Lateral Area**:
The lateral area consists of four triangular faces. The area of one triangle can be calculated using the formula:
\[
\text{Area of one triangle} = \frac{1}{2} \times \text{base} \times \text{height}
\]
In this case, the base of each triangle is the side length of the pyramid, and the height is the slant height.
\[
\text{Area of one triangle} = \frac{1}{2} \times 6 \times 7 = \frac{1}{2} \times 42 = 21 \, \text{m}^2
\]
Since there are four triangular faces, the total lateral area is:
\[
\text{Lateral Area} = 4 \times 21 = 84 \, \text{m}^2
\]

3. **Total Surface Area**:
Now, add the base area and the lateral area together:
\[
\text{Surface Area} = \text{Base Area} + \text{Lateral Area} = 36 + 84 = 120 \, \text{m}^2
\]

Thus, the surface area of the square pyramid is \( 120 \, \text{m}^2 \).