# Surface Area of a Square Pyramid

The surface area, or total surface area (TSA), of a square pyramid, is the entire space occupied by its five flat faces. It is measured in square units such as m2, cm2, mm2, and in2.

## Formula

The formula to calculate the surface area of a square pyramid also includes its lateral surface area (LSA). The formula is:

Lateral Surface Area (LSA) = 2bs, here b = base, s = slant height

Total Surface Area (TSA) = b2 + LSA

Let us solve some examples to understand the concept better.

## Solved Examples

Find the lateral and total surface area for a square pyramid with a base of 7 cm, and a slant height of 12 cm.

Solution:

As we know,
Lateral Surface Area (LSA) = 2bs, here b = 7 cm, s = 12 cm
LSA = 2 × 7 × 12
= 168 cm2
Total Surface Area (TSA) = b2 + LSA, here b = 7 cm, LSA = 168 cm2
TSA =72 + 168
= 217 cm2

Finding the lateral surface area for a square pyramid when BASE and HEIGHT are known

Find the lateral surface area for a square pyramid with a base of 4 cm, and a height of 6 cm.

Solution:

We will use an alternative formula here.
Lateral Surface Area (LSA) = ${b\sqrt{b^{2}+4h^{2}}}$, here b = 4 cm, h = 6 cm
LSA = ${4\sqrt{4^{2}+4\times 6^{2}}}$
= 50.6 cm2

Find the total surface area for a square based pyramid with a base of 8 cm, and a slant height of 18 cm.

Solution:

As we know,
Total Surface Area (TSA) = b2 + 2bs, here b = 8 cm, s = 18 cm
TSA =  82+ 2 × 8 × 18
= 352 cm2

Finding the total surface area for a square pyramid when BASE and HEIGHT are known

Find the total surface area for a square pyramid with a base of 3 cm, and a height of 13 cm.

Solution:

Here, we will use an alternative formula.
Total Surface Area (TSA) = ${b^{2}+b\sqrt{b^{2}+4h^{2}}}$, here b = 3 cm, h = 13 cm
TSA = ${3^{2}+3\sqrt{3^{2}+4\times 13^{2}}}$
= 87.51 cm2