Exercise 2 Page 834

The given solid is a prism.

The volume of a prism can be calculated using the following formula, where B is the area of the base and h is the height. V=Bh Let's first calculate the area of the base B. We can see that the base is a trapezoid, so we can use the known formula to find its area. B = 1/2h(b_1+b_2) From the diagram we can see that h=3in., b_1 = 15in. and b_2=7in. Let's calculate the area of the base.

B = 1/2h(b_1+b_2)

SubstituteIII

Substitute h = 3, b_1 = 15, b_2= 7

B = 1/2* 3*( 15+ 7)

▼

Simplify right-hand side

AddTerms

Add terms

B = 1/2*3*22

MoveRightFacToNumOne

1/b* a = a/b

B = 66/2

CalcQuot

Calculate quotient

B = 33

The base area of the prism is 33in^2. We are also given that the height equals 12in. Let's substitute these values into the formula and solve for V.

V=Bh

SubstituteII

B= 33, h= 12

V= 33* 12

Multiply

Multiply

V=396

The volume of the prism is 396in^3.