Exercise 21 Page 71

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

Surface Area

The given solid is a triangular prism.

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 We are given the lengths of all the base's sides. Let's add them to find the perimeter of the base. P=6+8+10=24cm Note that the base is a right triangle, so we can calculate its area using the formula for area of a triangle.

B=1/2bh

SubstituteII

b= 8, h= 6

B=1/2( 8)( 6)

▼

Simplify right-hand side

MoveRightFacToNumOne

1/b* a = a/b

B=48/2

CalcQuot

Calculate quotient

B=24

The area of the base is 24cm^2. Now we have enough information to find the surface area of the prism. Let's substitute P with 24, h with 5, and B with 24 into the formula.

S=Ph+2B

SubstituteValues

Substitute values

S=( 24)( 5)+2( 24)

▼

Simplify right-hand side

Multiply

Multiply

S=120+48

AddTerms

Add terms

S=168

The surface area of the prism is 168cm^2.

Volume

The volume of a prism can be calculated using the following formula. V=Bh Earlier we calculated that the area of the base B is 24cm^2. We are also given that the height equals 5cm. Let's substitute these values into the formula and solve for V.

V=Bh

SubstituteII

B= 24, h= 5

V=( 24)( 5)

Multiply

Multiply

V=120

The volume of the prism is 120cm^3.