Surface Area of Square Pyramid Calculator

Surface Area of a Square Pyramid

A square pyramid has a square base and four congruent triangular lateral faces. The total surface area is the base area plus the lateral surface area.

$$SA = a^2 + 2a\sqrt{\frac{a^2}{4} + h^2}$$

where $a$ is the base edge length and $h$ is the pyramid height. The slant height $l = \sqrt{a^2/4 + h^2}$ is the height of each triangular face.

The lateral surface area is $LSA = 2al$, and each triangular face has area $FA = \frac{a}{2} \cdot l$.

Example

A square pyramid with base edge 8 cm and height 6 cm has base area $8^2 = 64$ cm² and slant height $\sqrt{16 + 36} = \sqrt{52} \approx 7.21$ cm.

Frequently Asked Questions

How many faces does a square pyramid have?

A square pyramid has five faces: one square base and four congruent triangular lateral faces.

What is the slant height of a square pyramid?

The slant height is the distance from the apex to the midpoint of a base edge, measured along a triangular face. It is longer than the pyramid height unless the apex is directly above the center.

How is lateral surface area calculated?

The lateral surface area equals the sum of the four triangular faces: $LSA = 4 \times \frac{1}{2} \times a \times l = 2al$.

Can I use slant height instead of height?

Yes. If you know the slant height $l$, the total surface area is $SA = a^2 + 2al$.

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Surface Area of Square Pyramid Calculator

Surface Area of a Square Pyramid

Example

Frequently Asked Questions

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