Exercise 29 Page 659

We want to convert the lengths present on the following diagram to feet. Then, we want to find the area of the figure present on that diagram.

Converting between inches (in) and feet (ft) will involve using a conversion factor. 1ft/12inMultiplying the given lengths by this conversion factor will convert it to feet. Let's first convert 72 inches to feet.

72in * 1ft/12in

MoveLeftFacToNum

a*b/c= a* b/c

72in* 1ft/12in

Rewrite

Rewrite 72 as 6 * 12

6 * 12in* 1ft/12in

CancelCommonFac

Cancel out common factors

6 * 12 in * 1ft/12 in

SimpQuot

Simplify quotient

6*1ft/1

Multiply

6ft/1

DivByOne

a/1=a

6ft

72 inches is 6 feet. Now, let's convert 66 inches to feet.

66in * 1ft/12in

▼

Simplify

MoveLeftFacToNum

a*b/c= a* b/c

66in* 1ft/12in

CancelCommonFac

Cancel out common factors

66in * 1ft/12in

SimpQuot

Simplify quotient

66*1ft/12

Multiply

66ft/12

DivByOne

a/1=a

5.5ft

66 inches is 5.5 feet. Finally, let's convert 60 inches to feet.

60in * 1ft/12in

▼

Simplify

MoveLeftFacToNum

a*b/c= a* b/c

60in* 1ft/12in

Rewrite

Rewrite 60 as 5 * 12

5 * 12in* 1ft/12in

CancelCommonFac

Cancel out common factors

512 * in * 3ft/12 in

SimpQuot

Simplify quotient

5*1ft/1

Multiply

5ft/1

DivByOne

a/1=a

5ft

60 inches is 5 feet. Now, let's replace the lengths on our diagram with their values in feet.

Next, we want to find the area of the figure from the diagram. This figure is a trapezoid, so let's recall the formula for the area of a trapezoid. A = 1/2(b_1+b_2)h Here, b_1 and b_2 are the two bases of a trapezoid, and h is the height. In our case, the bases are 6 feet and 5.5 feet, and the height is 5 feet. Let's substitute these values into our formula and find the area of our figure!

A = 1/2(b_1+b_2)h

SubstituteValues

Substitute values

A = 1/2( 6+ 5.5) 5

AddTerms

Add terms

A = 1/2(11.5)5

Multiply

A = 1/2(57.5)

MoveRightFacToNumOne

1/b* a = a/b28.75

A = 57.5/2