Chapter 11.2, Problem 44SPR

To determine

To find:

The area of the rectangle.

Answer to Problem 44SPR

The area of rectangle is $7\sqrt{29}$ square units.

Explanation of Solution

Given information:

A rectangle with $R\left(-5,7\right)$ , $S\left(2,7\right)$ , $T\left(0,2\right)$ and $V\left(-7,2\right)$ .

Calculation:

Because the polygon is a rectangle, its opposite sides are the same length. Use the distance formula to find the length of two of the sides.

  $d=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}$

  $\begin{array}{c}RS=\sqrt{{\left(2+5\right)}^2+{\left(7-7\right)}^2}\\ =\sqrt{7^2}\\ =7\end{array}$

  $\begin{array}{c}RV=\sqrt{{\left(-7+5\right)}^2+{\left(2-7\right)}^2}\\ =\sqrt{{\left(-2\right)}^2+{\left(-5\right)}^2}\\ =\sqrt{4+25}\\ =\sqrt{29}\end{array}$

So, the area of rectangle is:

  $\begin{array}{c}A=\left(RS\right)\left(RV\right)\\ =7\sqrt{29}\end{array}$

Hence, the area of rectangle is $7\sqrt{29}$ square units.