Question

The square pyramid below has a height of 12 centimeters and a slant height of 20 centimeters. The square base of the pyramid has side lengths of 32 centimeters.



What is the lateral area of the pyramid?

384 cm2
640 cm2
768 cm2
1280 cm2

Answer 1

To find the lateral area of a square pyramid, we can use the formula:

\[
\text{Lateral Area} = \frac{1}{2} \times \text{Perimeter of base} \times \text{Slant height}
\]

1. **Calculate the Perimeter of the Base**:
The base of the pyramid is a square with side length \(s = 32 \text{ cm}\). The perimeter \(P\) of the square base is:

\[
P = 4s = 4 \times 32 = 128 \text{ cm}
\]

2. **Use the Slant Height**:
The slant height of the pyramid is given as \(l = 20 \text{ cm}\).

3. **Calculate the Lateral Area**:
Now we can substitute the perimeter and slant height into the formula for lateral area:

\[
\text{Lateral Area} = \frac{1}{2} \times P \times l = \frac{1}{2} \times 128 \times 20
\]

Calculating this:

\[
= \frac{1}{2} \times 128 \times 20 = 64 \times 20 = 1280 \text{ cm}^2
\]

Therefore, the lateral area of the pyramid is \( \boxed{1280 \text{ cm}^2} \).