Chapter 1, Problem 34SGR

To determine

To find the perimeter of quadrilateral $ABCD$

Answer to Problem 34SGR

21

Explanation of Solution

Given information:

Vertices of quadrilateral $A\left(-3,5\right)$ , $B\left(0,5\right)$ , $C\left(2,0\right)$ , $D\left(-5,0\right)$

Formula used:

  $perimeter=AB+BC+CD+DA$

To calculate distance between two points

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

Calculation: calculate distance between A (-3,5) and B(0,5) using distance formula

Substituting values in the formula

  $AB$ = $\sqrt{{\left(0+3\right)}^2+{\left(5-5\right)}^2}$

Solving it further

  $AB=\sqrt{9+0}$

Solving it further

  $AB=\sqrt{9}=3$

Now, calculate distance between B(0,5) and C(2,0)

Substituting values in the formula

  $BC=\sqrt{{\left(2-0\right)}^2+{\left(0-5\right)}^2}$

Solving it further

  $BC=\sqrt{4+25}$

Calculating the distance

  $BC=\sqrt{29}=5.3$

Now, calculate distance between C(2,0) and D(-5,0)

Substituting values in the formula

  $CD=\sqrt{{\left(-5-2\right)}^2+{\left(0-0\right)}^2}$

Solving it further

  $CD=\sqrt{49}=7$

Now, calculating the distance between D(-5,0) and A(-3,5)

Substituting values in the formula

  $DA=\sqrt{{\left(-3+5\right)}^2+{\left(5-0\right)}^2}$

Solving it further

  $DA=\sqrt{4+25}$

Solving further $DA=\sqrt{29}=5.3$

To calculate the perimeter of the quadrilateral add all the sides

  $perimeter=AB+BC+CD+DA$

Substituting values in the formula

  Perimeter = $3+5.3+7+5.3$

Calculating the final answer

  Perimeter = $20.6$

Or

21