Question

Here is a square pyramid and its net.

The lateral faces are congruent triangles. The base (shaded) is a square.
(All lengths are in centimeters.)

A. Find the area of the base of the pyramid.
B. Find the area of one lateral face of the pyramid
C. Use the net to find the lateral surface area of the pyramid. The base is not included.
D. Use the net to find the total surface area of the pyramid.

Answer 1

The area of the following part of the square pyramid is as follows:

a. area of the base of the pyramid = 9 cm²

b. area of one of the lateral face of the pyramid = 9.6 cm²

c. lateral surface area of the pyramid = 4(9.6) = 38.4 cm²

d. total surface area of the square based pyramid = 47.4 cm²

How to find the area of a square pyramid?

The area of the square base pyramid can be found as follows: The base of the pyramid is a square. Therefore,

a.

area of the base pyramid = l² = 3² = 3 × 3 = 9 cm²

b.

area of one of the lateral face of the pyramid = 1 / 2 bh

where

• b = base
• h = height

Therefore,

area of one of the lateral face of the pyramid = 1 / 2 × 3 × 6.4

area of one of the lateral face of the pyramid = 9.6 cm²

c.

lateral surface area of the pyramid = 4(9.6) = 38.4 cm²

d.

total surface area of the square based pyramid = 38.4 + 9 = 47.4 cm²

Answer 2

A. 9
`cm^(2)`

B. 9.6
`cm^(2)`

C. 38.4
`cm^(2)`

D. 47.4
`cm^(2)`

Explanation:

A. Area of the base of the pyramid = length x length

= 3 x 3

= 9
`cm^(2)`

B. Area of one lateral face of the pyramid = area of a triangle

=
`(1)/(2)` x base x height

=
`(1)/(2)` x 3 x 6.4

= 9.6
`cm^(2)`

Area of one lateral face of the pyramid = 9.6
`cm^(2)`

C. The lateral surface area of the pyramid = 4 x area of one lateral face

= 4 x 9.6

= 38.4

The lateral surface area of the pyramid = 38.4
`cm^(2)`

D. The total surface area of the pyramid = lateral surface area of the pyramid + area of the base

= 38.4 + 9

= 47.4

The total surface area of the pyramid = 47.4
`cm^(2)`