18 Questions
What is the shape of the base of a triangular pyramid?
Triangle
How is the surface area of a pyramid calculated?
By finding the sum of the areas of each of the polyhedron's flat faces
What is a characteristic of the triangular lateral sides of a regular pyramid?
They are all congruent
What is the shape of the lateral sides of a pyramid?
Triangles
What is the unit of measurement for the surface area of a pyramid?
Square units
What is the base area 'B' in the formula for the surface area of a pyramid?
area of the base
What is the lateral area of a pyramid?
sum of the areas of the lateral sides
In a pyramid, what is 'l' in the formula for the surface area?
slant length of the triangular side
What is the formula for the lateral area of a pyramid?
1/2 x P x l
What is the name of a pyramid with a hexagonal base?
Hexagonal pyramid
What is the shape of the lateral sides of a regular pyramid?
Triangle
What is the surface area of a pyramid?
The sum of the areas of the base and the lateral sides
What is the number of lateral sides of a regular pentagonal pyramid?
5
What is the purpose of a net in finding the surface area of a pyramid?
To visualize the individual faces of the pyramid
What is the perimeter of the base of a pyramid with a square base with sides of length 5 cm?
20 cm
What is the area of each lateral side of a pyramid with a square base of side length 5 cm and a slant length of 6 cm?
12.5 cm^2
What is the total surface area of a pyramid with a base area of 27.53 square cm, a base side length of 4 cm, and a slant length of 5 cm?
83.81 cm^2
What is the lateral area of a pyramid with a base perimeter of 14 cm and a slant length of 5 cm?
35 cm^2
Study Notes
Pyramid Definition
- A pyramid is a three-dimensional solid with a flat polygon base and triangular lateral sides that come to a point.
Types of Pyramids
- Triangular pyramid: base is a triangle
- Square pyramid: base is a square
- Pentagonal pyramid: base is a pentagon
- Hexagonal pyramid: base is a hexagon
- Octagonal pyramid: base is an octagon
Surface Area of a Pyramid
- Surface area is the sum of the areas of each face of the pyramid
- Formula: SA = B + (1/2)P*l
- Where SA is the total surface area, B is the base area, P is the perimeter of the base, and l is the slant length of the pyramid's triangular lateral sides
Finding the Surface Area of a Pyramid
- Find the area of the base (B)
- Find the lateral area (1/2)P*l
- Add the base area and lateral area to find the total surface area (SA)
Examples of Surface Area of a Pyramid
- Regular triangular pyramid: SA = B + (1/2)P*l
- Regular pentagonal pyramid: SA = B + (1/2)P*l
- Regular hexagonal pyramid: SA = B + (1/2)P*l
- Rectangular pyramid: SA = B + (1/2)P*l
Pyramid Definition
- A pyramid is a three-dimensional solid with a flat polygon base and triangular lateral sides that come to a point.
Types of Pyramids
- Triangular pyramid: base is a triangle
- Square pyramid: base is a square
- Pentagonal pyramid: base is a pentagon
- Hexagonal pyramid: base is a hexagon
- Octagonal pyramid: base is an octagon
Surface Area of a Pyramid
- Surface area is the sum of the areas of each face of the pyramid
- Formula: SA = B + (1/2)P*l
- Where SA is the total surface area, B is the base area, P is the perimeter of the base, and l is the slant length of the pyramid's triangular lateral sides
Finding the Surface Area of a Pyramid
- Find the area of the base (B)
- Find the lateral area (1/2)P*l
- Add the base area and lateral area to find the total surface area (SA)
Examples of Surface Area of a Pyramid
- Regular triangular pyramid: SA = B + (1/2)P*l
- Regular pentagonal pyramid: SA = B + (1/2)P*l
- Regular hexagonal pyramid: SA = B + (1/2)P*l
- Rectangular pyramid: SA = B + (1/2)P*l
Learn about pyramids, their characteristics, and how they are named based on their base shape. Understand the types of pyramids, including triangular, square, pentagonal, hexagonal, and octagonal pyramids.
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