Chapter 11.9, Problem 12PPS

a.

To determine

To calculate the area of the pool’s floor.

Answer to Problem 12PPS

  $388.8$ square feet.

Explanation of Solution

Given information:

The figure is can be divided into two trapezoids.

Trapezoid( $t_1$ ) has parallel side of $a_1=9$ feet and $b_1=16$ feet and height $h_1=14$ feet.

Trapezoid( $t_2$ ) has parallel side of $a_2=11$ feet and $b_2=17\frac{1}{2}$

  $=\frac{35}{2}$ feet and height $h_2=15$ feet.

Formula used: Area of trapezoid $t=\frac{a+b}{2}\times h$ where ‘a’ and ‘b’ are parallel sides while ‘h’ is the height.

Calculation:

Area of the trapezoid $t_1$

  $t_1=\frac{a_1+b_1}{2}\times h_1$

Formula of area of trapezoid

  $=\frac{9+16}{2}\times 14$

Simplify the expression

  $=25\times 7$

On multiplying

  $=175$ square feet

Area of the trapezoid $t_2$

  $t_2=\frac{a_2+b_2}{2}\times h_2$

Formula of area of trapezoid

  $=\frac{11+\frac{35}{2}}{2}\times 15$

Simplify the expression

  $=\frac{22+35}{2\times 2}\times 15$

This leads to

  $=\frac{57}{4}\times 15$

On multiplying

  $=213.75$ square feet

Now, add the two areas to get the area of the given figure.

  $=t_1+t_2$

  $=175+213.75$

  $=388.75$

Rounding to the nearest tenth.

  $=388.8$ square feet.

b.

To determine

To calculate the cost of the pool cover.

Answer to Problem 12PPS

  $\$661$

Explanation of Solution

Given information:

The per square foot cost of the cover is $1.70.

As obtained in sub-section a., total area of the pool is $388.8$ square feet.

Formula used: Multiplication of numbers.

Calculation:

Total cost is total area multiplied by cost per unit area.

  $=388.8\times 1.70$

The result is

  $=660.96$

On rounding off to the nearest tenth.

  $=\$661$