Exercise 15 Page 872

Consider the given solid.

The given solid is a rectangular prism. It has a length of 7 feet, a height of 8 feet, and a width of 3 feet. Let's first calculate the lateral area and then the surface area.

Lateral Area

To calculate the lateral area, we can use the known formula where h is the height of the prism and P is the perimeter of the base. L=Ph We are given the length of the sides of the base. Let's calculate the perimeter of the base. P&= 7+ 3+ 7+ 3 P&= 20 The perimeter of the base is 20 feet. We can substitute P= 20 and h= 8 in the formula to calculate L.

L=Ph

SubstituteII

P= 20, h= 8

L= 20( 8)

Multiply

Multiply

L=160

The lateral area is 160 square feet.

Surface Area

To calculate the surface area of a prism, we can use the known formula where P is the perimeter of the base, h is the height, and B is the area of the base. S=Ph+2B Note the base is a rectangle, so we can calculate its area using the formula for area of a rectangle.

B=l w

SubstituteII

l= 7, w= 3

B= 7( 3)

Multiply

Multiply

B=21

The area of the base is 21 square feet. Earlier, we found that Ph= 160 square feet. Let's substitute these values into the formula for the surface area of a prism.

S=Ph+2B

SubstituteII

Ph= 160, B= 21

S= 160+2(21)

▼

Simplify right-hand side

Multiply

Multiply

S=160+42

AddTerms

Add terms

S=202

The surface area of the prism is 202 square feet.