Surface Area of Pyramids

Show your work for each problem.

1.
What is the surface area formula for a square pyramid?
1. a)
2. b)
3. c)
4. d)
Answer:
The formula is because the base area is and the lateral area is .
2.
How many triangular faces does a square pyramid have?
1. a)3
2. b)6
3. c)5
4. d)4
Answer: 4
A square pyramid has 4 triangular faces, one for each side of the square base.
3.
A square pyramid has a base side of cm and slant height of cm. What is the area of ONE triangular face?
Answer: 10
Area of one triangular face = cm
4.
What is the base area of a square pyramid with a base side of cm?
Answer: 36
Base area = cm
5.
Find the surface area of a square pyramid with base side cm and slant height cm.
Answer: 85
1. Calculate the base area () 25
2. Calculate the lateral surface area () 60
3. Add them together for total surface area 85
6.
What is the difference between pyramid height and slant height?
1. a)Pyramid height is measured on a face
2. b)Slant height is always shorter
3. c)They are the same measurement
4. d)Pyramid height is vertical; slant height is along a face
Answer: Pyramid height is vertical; slant height is along a face
The pyramid height goes straight up from the center of the base to the apex. The slant height runs along a triangular face from a base edge midpoint to the apex.
7.
A pyramid has base side m and pyramid height m. What is the slant height?
Answer: 5
m
8.
A square pyramid has a total surface area of cm and base side cm. What is the slant height?
Answer: 10
Base area = cm. Lateral area = cm. So , meaning , so cm.
9.
Find the surface area of a square pyramid with base side m and pyramid height m.
Answer: 144
1. What is half of the base side? 4
2. Calculate slant height using 5
3. Calculate the base area 64
4. Calculate the lateral surface area () 80
5. Add for total surface area 144
10.
A tent has a square base of m and a pyramid height of m. Find the fabric needed for the walls (lateral area only).
Answer: 15
1. What is half of the base side? 1.5
2. Calculate slant height 2.5
3. Calculate lateral surface area () 15
11.
The lateral surface area of a square pyramid equals . What does this simplify from?
1. a)
2. b)
3. c)
4. d)
Answer:
12.
A square pyramid has base side cm and pyramid height cm. What is the total surface area?
Answer: 360
Slant height = cm. SA = cm
13.
Find the surface area of a regular tetrahedron (triangular pyramid where all edges equal cm).
Answer: 62.35
1. How many faces does a tetrahedron have? 4
2. Calculate the area of one equilateral triangle with side 6 using 15.59
3. Multiply by 4 for total surface area (round to 2 decimals) 62.35
14.
A pyramid model has base side m, pyramid height m. Glass costs 25 euros per m. What is the total cost to cover the entire pyramid?
Answer: 1664
1. Calculate half the base side 2
2. Calculate slant height using Pythagorean theorem 6.32
3. Calculate base area 16
4. Calculate lateral surface area () 50.56
5. Calculate total surface area 66.56
6. Multiply by cost per m² 1664
15.
A pyramid with base side has its slant height doubled. What happens to the lateral surface area?
1. a)It halves
2. b)It quadruples
3. c)It doubles
4. d)It stays the same
Answer: It doubles
Lateral area = . If doubles to , then lateral area = . But wait - this is , which means it doubles!
16.
Calculate the surface area of a square pyramid with base side cm and slant height cm.
Answer: 175
1. Calculate the base area () 49
2. Calculate the lateral surface area () 126
3. Add for total surface area 175
17.
What is the lateral surface area only (not including base) of a square pyramid with base side cm and slant height cm?
Answer: 192
Lateral area = cm
18.
A square pyramid has base side cm and pyramid height cm. Calculate the total surface area.
Answer: 1121
1. What is half of the base side? 10
2. Calculate slant height using 18.03
3. Calculate base area 400
4. Calculate lateral area () 721
5. Calculate total surface area 1121