Surface Area of a Square Pyramid Calculator

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.

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.

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

or, on simplifying:

, 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.

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

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:

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:

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

• SA = a² + 2×a×l

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

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

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.

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:

• Right rectangular pyramid calculator;
• Square pyramid calculator;
• Right square pyramid calc;
• Height of a square pyramid calculator;
• Rectangular pyramid volume calculator;
• Surface area of a rectangular pyramid calculator.