Table of Contents

Last modified on August 3rd, 2023

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 m^{2}, cm^{2}, mm^{2}, and in^{2}.

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)** =

Let us solve some examples to understand the concept better.

**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 cm^{2}

Total Surface Area (*TSA*) = b^{2} + *LSA*, here b = 7 cm, *LSA* = 168 cm^{2}

∴ *TSA* =7^{2} + 168

= 217 cm^{2}

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 cm^{2}

**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*) = b^{2} + 2bs, here b = 8 cm, s = 18 cm

∴ *TSA* = 8^{2}+ 2 × 8 × 18

= 352 cm^{2}

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 cm^{2}

Last modified on August 3rd, 2023