Chapter 11.9, Problem 8PPS

To determine

To calculate the area of the figure.

Answer to Problem 8PPS

  $39$ square feet.

Explanation of Solution

Given information:

The figure is can be divided into a trapezoid and a square.

Trapezoid has parallel side of $a=2$ feet and $b=5$ feet and height $h=4$ feet.

Square has a side of $a=5$ 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.

Area of square $s=a\times a$ where ‘a’ is the common side.

Calculation:

Area of the trapezoid

  $t=\frac{a+b}{2}\times h$

Formula of area of trapezoid

  $=\frac{2+5}{2}\times 4$

Simplify the expression

  $=7\times 2$

  $=14$ square feet

Area of square

  $s=a\times a$

Formula for area of square.

  $=5\times 5$

Simplify the expression

  $=25$ square feet.

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

  $=t+s$

  $=14+25$

  $=39$ square feet.