Table of Contents
Last modified on August 3rd, 2023
The surface area (or total surface area) of a pentagonal prism is the entire amount of space occupied by all its outer surfaces (or faces). It is measured in square units such as m2, cm2, mm2, and in2.
The formula is given below:
Let us solve some examples to understand the concept better.
Find the lateral and the total surface area of a pentagonal prism given in the figure.
As we know,
Lateral Surface Area (LSA) = 5bh, here b = 8 m, h = 12 m
∴ LSA = 5 × 8× 12
= 480 m2
Total Surface Area (TSA) = 5ab + LSA, here a = 5.505 m, LSA = 480
∴ TSA = 5 × 5.505 × 8 + 480
= 700.2 m2
Find the lateral area of a pentagonal prism with a base edge of 5.5 cm and height of 11 cm.
As we know,
Lateral Surface Area (LSA) = 5bh, here b = 5.5 cm, h = 11 cm
∴ LSA = 5 × 5.5 × 11
= 302.5 cm2
Finding the surface area of a pentagonal prism when the BASE EDGE and HEIGHT are known
Find the surface area of a pentagonal prism with a base edge of 11 cm and height 6 cm.
As we know,
Total Surface Area (TSA) = ${ 5bh+\dfrac{1}{2}\sqrt{5\left( 5+2\sqrt{5}\right) }b^{2} }$ , here b = 11 cm, h = 6 cm
 ∴ TSA = ${ 5\times 11\times 7+\dfrac{1}{2}\sqrt{5\left( 5+2\sqrt{5}\right) }\times 11^{2}}$
= 801.35 cm2
Last modified on August 3rd, 2023