Chapter 11.3, Problem 2PSA

a

To determine

To find : The area of the given trapezoid in the figure a

Answer to Problem 2PSA

The area is $A=75$

Explanation of Solution

Given information : The following information has been given

The base lengths are

  $a=12$ and $b=13$

The height between them is

  $h=6$

Formula used : The area of any trapezoid will be

  $A=\frac{a+b}{2}h$

Calculation : We know that the area of a trapezoid can be given as

  $A=\frac{a+b}{2}h$

Hence, we substitute the given values, and we get

  $A=\frac{12+13}{2}(6)=75$

b

To determine

To find : The area of the given trapezoid in the figure b

Answer to Problem 2PSA

The area is $A=72$

Explanation of Solution

Given information : The following information has been given

The median is $(m)=12$

The height between them is $(h)=6$

Formula used : The area of any trapezoid will be

  $A=\frac{a+b}{2}h$

Calculation : We know that the area of a trapezoid can be given as

  $A=\left(\frac{a+b}{2}\right)h=mh$

Where

  $m=\left(\frac{a+b}{2}\right)$ is median of the triangle.

Hence, we substitute the given values, and we get

  $A=12(6)=72$

c

To determine

To find : The area of the given trapezoid in the figure c

Answer to Problem 2PSA

The area is $A=78$

Explanation of Solution

Given information : The following information has been given

The base lengths are

  $a=17$ and $b=9$

The height between them is

  $h=6$

Formula used : The area of any trapezoid will be

  $A=\frac{a+b}{2}h$

Calculation : We know that the area of a trapezoid can be given as

  $A=\frac{a+b}{2}h$

Hence, we substitute the given values, and we get

  $A=\frac{17+9}{2}(6)=78$

d

To determine

To find : The area of the given trapezoid in the figure d

Answer to Problem 2PSA

The area is $A=312$

Explanation of Solution

Given information : The following information has been given

The base lengths are

  $a=21$ and $b=31$

The height between them is

  $h=12$

Formula used : The area of any trapezoid will be

  $A=\frac{a+b}{2}h$

Calculation : We know that the area of a trapezoid can be given as

  $A=\frac{a+b}{2}h$

Hence, we substitute the given values, and we get

  $A=\frac{21+31}{2}(12)=312$