Chapter 11.9, Problem 13PPS

a.

To determine

To calculate the area of the carpet space of the family room.

Answer to Problem 13PPS

  $354$ square feet.

Explanation of Solution

Given information:

Figure consists for a rectangle with length $l=23$ feet and breath $b=12$ feet.

It also consists of a trapezoid with parallel sides $l_1=10$ feet and $l_2=23-7$

  $=16$ feet and a height $h=18-12$

  $=6$ feet.

Formula used:

Area of rectangle $a=l\times b$ . Where ‘l’ is the length and ‘b’ is the breath.

Area of trapezoid $t=\frac{l_1+l_2}{2}\times h$ where $l_1$ and $l_2$ are the parallel sides and ‘h’ is the height.

Calculation:

Calculate the area of the rectangle and trapezoid. On adding the two, the area of the carpet space of the family room shall be derived.

  $a=l\times b$

Formula of rectangle

  $=23\times 12$

Multiply the length and breadth

  $=276$ square feet.

Next, calculate area of the trapezoid.

  $t=\frac{l_1+l_2}{2}\times h$

Formula of trapezoid.

  $=\frac{10+16}{2}\times 6$

Simplify the expression

  $=26\times 3$

On simplification

  $=78$ square feet.

Adding the two areas would give the area of the figure.

  $=a+t$

Putting the values of the areas

  $=276+78$

  $=354$ square feet.

b.

To determine

To calculate total costof carpet for Mr. Reyes’ room.

Answer to Problem 13PPS

$ $796.5$ .

Explanation of Solution

Given information:

One square foot of carpet costs $2.25.

From sub-part a., total area room floor $=354$ square feet

Cost for the same shall be the product of the cost per square foot multiplied by the total floor area.

  $=\$2.25\times 354$

On multiplying

  $=\$796.5$

This is the total cost.