Page 11 - Math Course 2 (Book 2)

Geometric Surface Area: Prisms

Real World Example
Let’s Begin

SCULPTURE
A solid block of marble will be used for a sculpture.
1
Lateral Area of a Pentagonal Prism If the block is 3 feet wide, 4 feet long, and 9 feet
2
Example high, find the surface area of the block.

3 ft 4 ft
Find the lateral area of the regular hexagonal prism. The block is shaped like
a rectangular prism.
The bases are regular hexagons. So the perimeter of
one base is 6(5) or 30 centimeters. 1
9 ft
2

The perimeter of a base is 2(3) + 2(4) or 14 feet.
5 cm 12 cm The area of a base is 3(4) or 12 square feet.

L = Ph Lateral area of a prism T = L + 2B Formula for surface area
= (30)(12) P = 30, h = 12
1
1
= 360 Multiply. = 14 (9 ) + 2(12) P = 14, h = 9 , B = 12
2 2
= 157 Simplify.
The lateral area is 360 square
Answer
centimeters. The surface area of the block
Answer
of marble is 157 square feet.
Surface Area of a Prism

Example Your Turn!

Lateral Area of a Pentagonal Prism
Find the surface area of the square prism.
Find the lateral area of the regular octagonal prism.

A. 162 cm 2
B. 216 cm 2
6 cm 12 cm C. 324 cm 2

D. 432 cm 2
6 cm
L = Ph Surface area of a prism
= (24)(12) + 2(36) Substitution
= 360 Simplify.

The surface area is 360
Answer Answer
square centimeters.

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