Chapter 9.6, Problem 17PSB

a.

To determine

To find: The most descriptive name for quadrilateral PQRS.

Answer to Problem 17PSB

The most descriptive name for quadrilateral PQRS is trapezoid.

Explanation of Solution

Given:

Coordinates of P, Q, R and S are $\left(-4,0\right),\left(-1,4\right),\left(8,4\right)$ and $\left(11,0\right)$

Concept used:

Here, we are using the concept of distance formula.

Calculation:

Here, the formula is

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

Now, $PR=\sqrt{{\left(8+4\right)}^2+{\left(4-0\right)}^2}$

  $PR=\sqrt{16+144}$

  $PR=12.64$

And, $QS=\sqrt{{\left(11+1\right)}^2+{\left(0-4\right)}^2}$

  $QS=\sqrt{16+144}$

  $QS=12.64$

Conclusion: The diagonals are equal. So, we can say that PQRS is trapezoid.

b.

To determine

To find: The area of PQRS

Answer to Problem 17PSB

The area of PQRS is $80$

Explanation of Solution

Given: Coordinates of P, Q, R and S are $\left(-4,0\right),\left(-1,4\right),\left(8,4\right)$ and $\left(11,0\right)$

Formula used: Here, the formula is

Area = $\frac{1}{2}\times d_1\times d_2$

Calculation: $d_1=d_2=12.64$ (find above)

So, Area = $\frac{1}{2}\times 12.64\times 12.64$

  →$80$

Conclusion: Hence, the area of PQRS is $80$

c.

To determine

To Calculate: The Lengths of PR andQS ,

Answer to Problem 17PSB

Lengths of PR and QS are $12.64$

Explanation of Solution

Given:Coordinates of P, Q, R and S are $\left(-4,0\right),\left(-1,4\right),\left(8,4\right)$ and $\left(11,0\right)$

Calculation: Here, PR=QS= $12.64$ (find above)

Conclusion: Hence, lengths of PR and QS are $12.64$