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```Lateral Area of a Regular Pyramid
Find the lateral area of
the square pyramid.
Lateral area of a regular
pyramid
P = 2.5 ● 4 or 10, ℓ = 5
Answer: The lateral area is 25 square centimeters.
Find the lateral area of the square pyramid.
A. 54 in2
B. 64 in2
C. 108 in2
D. 132 in2
Surface Area of a Square Pyramid
Find the surface area of the square pyramid to the
nearest tenth.
Step 1
Find the slant height
c2 = a2 + b2
Pythagorean Theorem
ℓ2 = 62 + 42
a = 6, b = 4, and c = ℓ
ℓ=
Simplify.
Surface Area of a Square Pyramid
Step 2
Find the perimeter and area of the base.
P = 4 ● 8 or 32 m
Step 3
Find the surface area of the pyramid.
__
S = 1 Pℓ + B
2
1 (32)
= __
2
≈ 179.4
A = 82 or 64 m2
Surface area of a
regular pyramid
+ 64
P = 32, ℓ =
,
B = 64
Use a calculator.
179.4 square meters.
Find the surface area of the square
pyramid to the nearest tenth.
A. 96 in2
B. 124.3 in2
C. 138.5 in2
D. 156 in2
Surface Area of a Regular Pyramid
Find the surface area of the regular pyramid.
Round to the nearest tenth.
Step 1
Find the perimeter of the base.
P = 6 ● 10.4 or 62.4 cm
Surface Area of a Regular Pyramid
Step 2
Find the length of the apothem and the
area of the base.
360° or
A central angle of the hexagon is ______
6
60°, so the angle formed in the triangle is
30°.
Surface Area of a Regular Pyramid
tan 30° =
Write a trigonometric ratio to
find the apothem a.
a=
Solve for a.
a ≈ 9.0
Use a calculator.
A=
Area of a regular polygon
≈
Pa
(62.4)(9.0) Replace P with 62.4 and a
width 9.0.
≈ 280.8
Multiply.
So, the area of the base is approximately 280.8 cm2.
Surface Area of a Regular Pyramid
Step 3
Find the surface area of the pyramid.
S=
≈
Pℓ + B
Surface area of regular
pyramid
(62.4)(15) + 280.8
P = 62.4, ℓ = 15, and
B ≈ 280.8
≈ 748.8
Simplify.
748.8 cm2.
Find the surface area of the regular pyramid. Round
to the nearest tenth.
A. 198 in2
B. 228.5 in2
C. 255.5 in2
D. 316.3 in2
Lateral Area of a Cone
ICE CREAM A sugar cone has an altitude of
8 inches and a diameter of
inches. Find the
lateral area of the sugar cone.
If the cone has a diameter of
then the
Use the altitude and
the radius to find the slant height with the Pythagorean
Theorem.
Lateral Area of a Cone
Step 1
Find the slant height ℓ.
ℓ2 = 82 + 1.252
Pythagorean Theorem
ℓ2 ≈ 65.56
Simplify.
ℓ ≈ 8.1
Step 2
Take the square root of
each side.
Find the lateral area L.
L = rℓ
Lateral area of a cone
≈ (1.25)(8.1) r = 1.25 and ℓ ≈ 8.1
≈ 31.8
31.8 square inches.
HATS A conical birthday hat has an altitude of
6 inches and a diameter of 4 inches. Find the lateral
area of the birthday hat.
A. 39.7 in.2
B. 43.6 in.2
C. 48.2 in.2
D. 53.1 in.2
Surface Area of a Cone
Find the surface area of
the cone. Round to the
nearest tenth.
Estimate: S ≈ 3 ● 1.5 ● 3 + 3 ● 2 or 19.5 cm2
S = rℓ + r2
Surface area of a cone
= (1.4)(3.2) + (1.4)2 r = 1.4 and ℓ = 3.2
≈ 20.2