Chapter 11.2, Problem 34PPS

To determine

Find whether either of them is correct.

Answer to Problem 34PPS

Madeline is correct

Explanation of Solution

Given:

A and M want to draw a trapezoid that has a height of 4 units and an area of 18 square units. A says that only one trapezoid will meet the criteria. M disagrees and thinks that she can draw several different trapezoids with a height of 4 units and an area of 18 square units.

Calculation:

The area of a trapezoid with bases $b_1\text{ and }{b}_2$ and height h :

  $\begin{array}{l}A=\frac{1}{2}\left(b_1+b_2\right)h\\ \Rightarrow 18=\frac{1}{2}\left(b_1+b_2\right)\mathrm{4..................}[\text{given h=4 and A=18]}\\ \Rightarrow 18=2\left(b_1+b_2\right)\\ \Rightarrow b_1+b_2=\mathrm{9............................}[\text{divide each side by 2]}\end{array}$

There are infinite possibilities of trapezoids that have sum of the bases 9 , that have height 4 and area 18 square units.

Hence, Madeline is correct.