Transcript Surface Area of a Regular Pyramid

1. Find the surface area of a cylinder with r = 10 and
h = 6. Round to the nearest tenth.
2. Find the surface area of a cylinder with r = 4.5 and
h = 6.3. Round to the nearest tenth.
3. Find the surface area of the cylinder
shown to the nearest tenth.
4. What is the height of a cylinder with
radius of 4 centimeters and surface
area of 80 square centimeters?
• Find lateral areas of regular pyramids.
• Find surface areas of regular pyramids.
• regular pyramid
• slant height
Find Lateral Area
CANDLES A candle store offers a pyramidal candle
that burns for 20 hours. The square base is 6
centimeters on a side and the slant height of the
candle is 22 centimeters. Find the lateral area of the
candle.
We need to find the lateral area of the square pyramid.
The sides of the base measure 6 centimeters, so the
perimeter is
Find Lateral Area
Lateral area of a regular pyramid
Multiply.
Answer: The lateral area of the candle is 264 square
centimeters.
CAMPING A tent in the shape of a pyramid is put up
by two campers. The square base is 7 feet on a side
and the slant height of the tent is 7.4 feet. Find the
lateral area of the tent.
A. 25.9 ft2
B. 51.8 ft2
C. 103.6 ft2
D. 207.2 ft2
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B.
C.
D.
A
B
C
D
Surface Area of a Square Pyramid
Find the surface area of the square pyramid. Round
to the nearest tenth if necessary.
To find the surface area, first
find the slant height of the
pyramid. The slant height is
the hypotenuse of a right
triangle with legs that are
the altitude and a segment
with a length that is one-half
the side measure of the
base.
Surface Area of a Square Pyramid
Pythagorean Theorem
Simplify.
Now find the surface area of a square pyramid. The
perimeter of the base is
and the area
of the base is
Surface Area of a Square Pyramid
Surface area of a square
pyramid
Use a calculator.
Answer: The surface area is 179.4 square meters to
the nearest tenth.
Find the surface area of the
square pyramid to the nearest
tenth.
A. 73.8 m2
B. 89.8 m2
C. 163.5 m2
D. 696 m2
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2.
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4.
A
B
C
D
Surface Area of a Regular Pyramid
Find the surface area of the regular pyramid. Round
to the nearest tenth.
The altitude, slant height,
and apothem form a right
triangle. Use the
Pythagorean Theorem to find
the apothem. Let x represent
the length of the apothem.
Surface Area of a Regular Pyramid
Pythagorean Theorem
Simplify.
Now find the length of the sides of the base. The central
angle of the hexagon measures
Let a
represent the measure of the angle formed by a radius
and the apothem.
Surface Area of a Regular Pyramid
Use trigonometry to find the length
of the sides.
Multiply each side by 9.
Multiply each side by 2.
Use a calculator.
Surface Area of a Regular Pyramid
Next, find the perimeter and area of the base.
Surface Area of a Regular Pyramid
Finally, find the surface area.
Surface area of a regular
pyramid
Simplify.
Answer: The surface area is approximately 748.2
square centimeters.
Find the surface area of the regular pentagonal
pyramid.
A. 236.1 cm2
B. 326.9 cm2
C. 90.8 cm2
D. 417.7 cm2
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A
B
C
D