Table of Contents

Last modified on August 3rd, 2023

The surface area, or total surface area (TSA), of a triangular pyramid, is the entire space occupied by its four faces. It is measured in square units such as m^{2}, cm^{2}, mm^{2}, and in^{2}.

The formula is:

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

**Lateral Surface Area (LSA) = ${\dfrac{1}{2}Ps}$**, here P = base perimeter, s = slant height

∴ **Total Surface Area** **( TSA) = B + LSA**

Let us solve some example to understand the above concept better.

**Find the surface area of a regular triangular pyramid with a base area of 43 cm ^{2}, a base perimeter of 30 cm, and a slant height of 8 cm.**

Solution:

As we know,

Total Surface Area (*TSA*) = ${B+\dfrac{1}{2}Ps}$, here B = 43 cm^{2}, P = 30 cm, s = 8 cm

∴ *TSA* = ${43+\dfrac{1}{2}\times 30\times 8}$,

= 163 cm^{2}

**Calculate the lateral and total surface area of a triangular-based pyramid with a base of 20 cm, a base height of 12 cm, and a slant height of 19 cm.**

Solution:

As we know,

Lateral Surface Area (*LSA*) = ${\dfrac{1}{2}Ps}$,

P = 3 × b, here b = 20 cm

∴ *LSA* = ${\dfrac{3}{2}bs}$, here b = 20 cm, s = 14 cm

= ${\dfrac{3}{2}\times 20\times 14}$

= 570 cm^{2}

Total Surface Area (*TSA*) = B + *LSA*

Now, B = ${\dfrac{1}{2}bH}$, here b = 20 cm, H = 12 cm

∴ ${TSA=\dfrac{1}{2}bH+LSA}$, here b = 20 cm, H = 12 cm, *LSA* = 570 cm^{2}

∴ ${TSA=\dfrac{1}{2}\times 20\times 12+570}$

= 690 cm^{2}

Finding the surface area of a regular (equilateral) triangular pyramid when the **BASE** and **SLANT** **HEIGHT** are known

**Find the surface area of a regular** **triangular pyramid with a base of 16 cm and a slant height of 19 cm.**

Solution:

Here, we will use an alternative formula.

Total Surface Area (*TSA*) = ${\dfrac{\sqrt{3}}{4}b^{2}+\dfrac{1}{2}\times 3bs}$, here b = 16 cm, s = 19 cm

∴ *TSA* = ${\dfrac{\sqrt{3}}{4}\times 16^{2}+\dfrac{1}{2}\times 3\times 16\times 19}$

= 566.85 cm^{2}

Last modified on August 3rd, 2023