# Surface Area of a Square Pyramid Calculator

Created by Mehjabin Abdurrazaque
Reviewed by Dominik Czernia, PhD
Last updated: Feb 02, 2023

Are you in search of a surface area of a square pyramid calculator to estimate all types of areas of the Great pyramid?! If yes, you're in the right place. You can calculate the total surface area, base area, lateral surface area, and face area of any square pyramid using our tool.

We also discuss how to find the surface area of a square pyramid using slant height and base length and how to calculate surface area using slant height and base perimeter. You can also find answers to some interesting numerical problems like the surface area of a pyramid of Giza and the amount of groundsheet required for any tent.

## How do I calculate the surface area of a square pyramid?

To find the surface area of a square pyramid:

1. Determine how many faces are there on a square pyramid: there are 4 triangular faces. Sum up their areas.
2. Find the area of a square base.
3. Add up 4 triangular faces area to 1 square base area to find the surface area of a square pyramid.

## What is the formula for the surface area of a square pyramid?

The formula to calculate the surface area of a square pyramid is:

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

or, on simplifying:

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

, where:

• SA is the surface area of the square pyramid;
• a is the length of the base edge; and
• h is the height of the square pyramid.

## How do I calculate the base area of a square pyramid?

The base of a square pyramid is a square. Hence, the base area of the square pyramid of base edge a is a2.

## How to find the lateral area of a square pyramid

First of all, let's explain what the lateral area of a square pyramid is. The lateral surface area or lateral area of a square pyramid is the total area of its 4 triangular faces. We calculate the lateral area as:

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

💡 The total surface area of a three-dimensional object is the sum of the base area and the lateral surface area!

• SA = BA + LSA

## How do I find the face area of a square pyramid?

The face area of a square pyramid is the area of one of its four triangular faces. We calculate the area of a triangular face, the face area (FA), using the formula:

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

💡 The lateral surface area is the sum of the areas of four triangular faces:

• LSA = 4 × FA

## How to find the surface area of a square pyramid using slant height

To find the surface area using the slant height, we use the formula:

• SA = a2 + 2×a×l

🔎 Proof: The surface area of a square pyramid is the sum of the areas of its square base and four triangular faces:

• SA = BA + (4 × FA)

The area of a triangle is half of the product of its base length (a) and height (l):

• FA = a×l/2

Therefore, the area of four triangular faces or the lateral surface area of the square pyramid is:

• 4 × FA = 2 × a × l

Thus, the lateral surface area (LSA) of the square pyramid of slant height l is

• LSA = 2 × a × l

and the total surface area is

• SA = a2 + 2 × a × l

## How to use the surface area of a square pyramid calculator

❓ The Pyramid of Giza has a height of 480 feet. If the length of each side of the base is approximately 756 feet, what is its total surface area?

Okay, let's see how to use this total surface area of a square pyramid calculator to solve the problem given above:

1. Identify the measurements:

• Height (h) = 480 ft
• Base edge (a) = 756 ft
2. Switch the units from cm to ft and cm2 to ft2 (or the desired units for the area) using the drop-down list near each variable in the square-based pyramid surface area calculator.

3. Enter the values for height (480 ft) and base edge (756 ft).

4. Ta-da! You got the results in no time! Our tool uses the surface area square pyramid formula to find:

• Slant height (l) = 611 ft
• Total surface area (SA) = 1,495,322 ft2
• Base area (BA) = 571,536 ft2
• Lateral surface area (LSA) = 923,786 ft2
• Face area (FA) = 230,947 ft2

## FAQ

### How many faces are on a square pyramid?

A square pyramid has 5 faces: 4 equal triangles (side faces) and 1 square (base face).

### How do I calculate the surface area of a square pyramid using its base perimeter?

The surface area of a square pyramid is half of the product of its base perimeter and its slant height:

• SA = P × l / 2

where P is the base perimeter and l is the slant height.

### How many square meters of groundsheet is required for a tent of base 5m and height 1.8m?

You need (5 m)2 = 25 m2 of groundsheet for the tent of base length 5 m irrespective of its height. The amount of groundsheet in square meters is the base area of the tent. The base area of a tent is BA = a2, where a is the base length.

After learning how to calculate the surface area of a square pyramid, you might want to check our other square pyramid calculators:

Mehjabin Abdurrazaque
Base edge (a)
in
Height (h)
in
Slant height (l)
in
Base perimeter (P)
in
Surface area
Total surface area (SA)
in²
Base area (BA)
in²
Lateral surface area (LSA)
in²
Face area (FA)
in²
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