Exercise 53 Page 870

Use the formulas for the lateral and surface area.

Lateral Area: 126 cm^2
Surface Area: 175 cm^2

Practice makes perfect

The given solid is a pyramid.

To calculate the lateral area of a pyramid, we can use the known formula where P is the perimeter of the base and l is the slant height. L=1/2PlThe base of the pyramid is a square with the side length of 7cm. Let's calculate its perimeter!

P = 4s

Substitute

s= 7

P = 4( 7)

Multiply

P = 28

We are also given that the slant height l is 9cm. Let's substitute all of these values into the formula for the lateral area and calculate it.

L = 1/2 P l

SubstituteII

P= 28, l= 9

L = 1/2 ( 28)( 9)

Multiply

L = 126

We have found that the lateral area is 126cm^2. To find the surface area, all we have to do is add the base area B to the lateral area L. The base is a square with a side length of 7cm. The area of the square equals the squared length of the side.

B = s^2

Substitute

s= 7

B = ( 7)^2

CalcPow

Calculate power

B = 49

We can now calculate the surface area.

S = L + B

SubstituteII

L= 126, B= 49

S = 126+ 49