Exercise 1 Page 827

Let's first calculate the lateral area and then the surface area.

Lateral Area

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=1/2Pl The base of the pyramid is a square with a side length of 16cm. Let's calculate its perimeter! P=4s ⇒ P=4( 16)= 64cm We are also given that the slant height l is 12cm. Let's substitute all of these values into the formula for the lateral area and calculate it.

L=1/2Pl

SubstituteII

P= 64, l= 12

L=1/2( 64)( 12)

▼

Simplify right-hand side

MoveRightFacToNumOne

1/b* a = a/b

L=64/2(12)

CalcQuot

Calculate quotient

L=32(12)

Multiply

Multiply

L=384

The lateral area of the pyramid is 384 cm^2.

Surface Area

To calculate the surface area of a pyramid, we need to calculate the sum of the lateral area L and the area of the base B. S=L+B Recall that the base of the pyramid is a square with a side length of 16cm. The area of the square equals the squared length of the side. B=s^2 ⇒ B= 16^2= 256cm^2 Let's substitute L= 384 and B= 256 into the formula for the surface area and calculate it.

S=L+B

SubstituteII

L= 384, B= 256

S= 384+ 256

AddTerms

Add terms

S=640

The surface area of the pyramid is 640 cm^2.