Question

Surface area of pyramids practice lesson 4 unit 8

Answer 1

To find the surface area of a pyramid, we need to calculate the area of each face and then sum them up.

Let's start with a regular pyramid, where the base is a square.

The formula for the surface area of a regular pyramid with a square base is:

Surface Area = Base Area + (Base Perimeter x Slant Height / 2)

1. Example 1:
Given a regular pyramid with a square base:
Base length = 5 cm
Slant height = 8 cm

First, calculate the base area:

Base Area = Base length x Base length = 5 cm x 5 cm = 25 cm^2

Next, calculate the base perimeter:

Base Perimeter = 4 x Base length = 4 x 5 cm = 20 cm

Finally, calculate the surface area:

Surface Area = Base Area + (Base Perimeter x Slant Height / 2)
Surface Area = 25 cm^2 + (20 cm x 8 cm / 2)
Surface Area = 25 cm^2 + (160 cm^2 / 2)
Surface Area = 25 cm^2 + 80 cm^2
Surface Area = 105 cm^2

Therefore, the surface area of the given regular pyramid is 105 cm^2.

2. Example 2:
Given a regular pyramid with a square base:
Base length = 10 cm
Slant height = 15 cm

First, calculate the base area:

Base Area = Base length x Base length = 10 cm x 10 cm = 100 cm^2

Next, calculate the base perimeter:

Base Perimeter = 4 x Base length = 4 x 10 cm = 40 cm

Finally, calculate the surface area:

Surface Area = Base Area + (Base Perimeter x Slant Height / 2)
Surface Area = 100 cm^2 + (40 cm x 15 cm / 2)
Surface Area = 100 cm^2 + (600 cm^2 / 2)
Surface Area = 100 cm^2 + 300 cm^2
Surface Area = 400 cm^2

Therefore, the surface area of the given regular pyramid is 400 cm^2.

Practice these calculations with various values to improve your understanding of finding the surface area of pyramids.