EXAMPLE 1 Find the area of a lateral face of a pyramid

SOLUTION

Use the Pythagorean Theorem to find the slant height l.

l2 =152 +82

Write formula.l2 = h2 +( b)212

A regular square pyramid has a height of 15 centimeters and a base edge length of 16 centimeters. Find the area of each lateral face of the pyramid

Substitute for h and b.12

EXAMPLE 1 Find the area of a lateral face of a pyramid

l = 17 Find the positive square root.

l2 = 289 Simplify.

A = bl = (16)(17) = 136 square centimeters.12

12

The area of each triangular face is

ANSWER

EXAMPLE 2 Find the surface area of a pyramid

SOLUTION

Find the surface area of the regular hexagonal pyramid.

First, find the area of the base using the formula for

the area of a regular polygon, aP. The apothem a of

the hexagon is 5√ 3 feet and the perimeter P is 6 10 =

60 feet. So, the area of the base B is (5√ 3)(60)

= 150√ 3 square feet. Then, find the surface area.

12

12

EXAMPLE 2 Find the surface area of a pyramid

Formula for surface area of regular pyramid.

≈ 679.81

Substitute known values.

Simplify.

Use a calculator.

= 150√ 3 + (60)(14)12

= 150√ 3 + 420

S = B + Pl12

The surface area of the regular hexagonal pyramid is about 679.81 ft2.

ANSWER

GUIDED PRACTICE for Examples 1 and 2

1. Find the area of each lateral face of the regular pentagonal pyramid shown.

Use the Pythagorean theorem to find the slant height l

SOLUTION

GUIDED PRACTICE for Examples 1 and 2

l2 = (4.8) + (5.5)2

Write formula.l2 = h2 +( b)212

Substitute for h and b.12

Find the positive square root.l2 = 7.5

The area of each lateral face is A = bl = (8) (7.3) =29.2m2

12

12

ANSWER

GUIDED PRACTICE for Examples 1 and 2

2. Find the surface area of the regular pentagonal pyramid shown.

First find the area of the base using the formula for the area of a regular polygon, AP the apothem a of the pentagon is 5.5m and the perimeter p is 5.8 = 40m so , the area of the base is (5.5) (40) = 110m. Then find the surface area

12

12

SOLUTION

GUIDED PRACTICE for Examples 1 and 2

S = b + pl 12

12= 110 + (40)7.3

= 256

Formula for surface area of regular pyramid.

Substitute known values.

Use a calculator.

The surface area of the rectangle pentagon pyramid is 256m2

ANSWER