Table of Contents

Last modified on March 28th, 2023

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

The general formula is:

**Surface Area (SA) = ${B+\dfrac{1}{2}Ps}$**, here B = base area, P = base perimeter, s = slant height,

Also **${\dfrac{1}{2}Ps}$** = lateral surface area (

∴ *SA* = B + *LSA*

However, there are specific formulas to calculate the surface area of different pyramids. They are given below:

Let us solve some examples involving the above formulas.

**Calculate the surface area of a triangular pyramid with a base area of 24 cm ^{2}, a base perimeter of 12 cm, and a slant height of 16 cm.**

Solution:

As we know,

Surface Area (SA) = ${B+\dfrac{1}{2}Ps}$, here B = 24 cm^{2}, P = 12 cm, s = 16 cm

∴ *SA* = ${24+\dfrac{1}{2}\times 12\times 16}$

= 120 cm^{2}

Finding the surface area of a triangular pyramid when **BASE**, **BASE HEIGHT**, and **SLANT HEIGHT** are known.

**Find the total surface area of a regular triangular pyramid with a slant height of 10 cm, base of 6 cm, and a base height of 5.2 cm.**

Solution:

As we know,

Total Surface Area (*TSA*) = ${\dfrac{1}{2}bH+\dfrac{3}{2}bs}$, here b = 6 cm, H = 5.2 cm, s = 10 cm

∴ *TSA* = ${\dfrac{1}{2}\times 6\times 5.2+\dfrac{3}{2}\times 6\times 10}$

= 285.6 cm^{2}

**Find the lateral and total surface area of a square pyramid with a base of 6 cm and a slant height of 7.3 cm.**

Solution:

As we know,**Lateral Surface Area ( LSA) = 2bs, **here b = 6 cm, s = 7.3 cm

∴

= 87.6 cm

∴

= 123.6 cm

**Find the total surface area of a rectangular pyramid with a base of 7 cm and 9 cm, and a height of 11 cm.**

Solution:

As we know,

Total Surface Area (*TSA*) = ${lw+\dfrac{1}{2}w\sqrt{4h^{2}+l^{2}}+\dfrac{1}{2}l\sqrt{4h^{2}+w^{2}}}$, ** **here l = 9 cm, w = 7 cm, h = 11 cm

∴*TSA* = ${9\times 8+\dfrac{1}{2}\times 7\sqrt{4\times 11^{2}+9^{2}}+\dfrac{1}{2}\times 9\sqrt{4\times 11^{2}+7^{2}}}$

= 250.08 cm^{2}

**Find the total surface area of a pentagonal pyramid with a base of 3 cm, apothem of 2.06 cm, and a slant height of 4 cm.**

Solution:

As we know,

Total Surface Area (*TSA*) = ${\dfrac{5}{2}b\left( a+s\right)}$,** **here b = 3 cm, a = 2.06 cm, s = 4 cm

∴*TSA* = ${\dfrac{5}{2}\times 3\times \left( 2.06+4\right)}$

= 45.45 cm^{2}

**Find the total surface area of a hexagonal pyramid with a base of 4 cm, apothem of 3.46 cm, and a slant height of 13 cm.**

Solution:

As we know,**Total Surface Area ( TSA) = 3ab + 3bs**, here a = 3.46 cm, b = 4 cm, s = 13 cm

∴

= 197.52 cm

Last modified on March 28th, 2023