Chapter 11.3, Problem 10PSB

a.

To determine

To calculate:The length of PQ

Answer to Problem 10PSB

The length of PQ is $10$

Explanation of Solution

Given:

The area of triangle PQS is $25$

The median of trapezoid PQRS is $14$ and

Base $\overline{RS}$ measures $18$

Concept used:

Here, we are using the formula

Median = $\frac{1}{2}\left(lowerbase+upperbase\right)$

Calculation: Here, Median = $\frac{1}{2}\left(lowerbase+upperbase\right)$

  $14=\frac{1}{2}\left(18+PQ\right)$

  $28=18+PQ$

  $PQ=10$

Conclusion: Hence, the length of PQ is $10$

b.

To determine

To calculate:The height to base $\overline{PQ}$ of $\Delta PQS$

Answer to Problem 10PSB

The height to base $\overline{PQ}$ of $\Delta PQS$ is $5$

Explanation of Solution

Given:

The area of triangle PQS is $25$

The median of trapezoid PQRS is $14$ and

Base $\overline{RS}$ measures $18$

Formula used:

Here, the formula is

Area of triangle = $\frac{1}{2}\times base\times height$

Calculation:

Here,

Area = $\frac{1}{2}\times base\times height$

  $25=\frac{1}{2}\times 10\times height$

  $height=5$

Conclusion: Hence, the height to base $\overline{PQ}$ of $\Delta PQS$ is $5$

c.

To determine

To calculate:The height of trapezoid PQRS

Answer to Problem 10PSB

The height of trapezoid PQRS is $5$

Explanation of Solution

Given:

The area of triangle PQS is $25$

The median of trapezoid PQRS is $14$ and

Base $\overline{RS}$ measures $18$

Calculation:

Here, the height of $\Delta PQS$ = height of trapezoid PQRS

Conclusion: Hence, the height of trapezoid PQRS is $5$

d.

To determine

To calculate: The area of trapezoid PQRS

Answer to Problem 10PSB

The area of trapezoid PQRS is $70$

Explanation of Solution

Given:

The area of triangle PQS is $25$

The median of trapezoid PQRS is $14$ and

Base $\overline{RS}$ measures $18$

Formula used:

Here, the formula is

Area of trapezoid = $\frac{1}{2}\left(a+b\right)\times h$

(Where, “ a ” is upper base, “ b ”is lower base and “ h” is height)

Calculation: Here, area of trapezoid = $\frac{1}{2}\left(a+b\right)\times h$

(Where, “ a ” is upper base, “ b ” is lower base and “ h ”is height)

Area = $\frac{1}{2}\left(10+18\right)\times 5$

→ $70$

Conclusion: Hence, the area of trapezoid PQRS is $70$