Chapter 11.3, Problem 4CE

To determine

To Explain: Why the area of the trapezoid can be given by the formula $Area=height\times median$ .

Explanation of Solution

Given: $Area=height\times median$

  

Area of Trapezoid is $A_1+A_2$

Area of triangles $A_{1}and{A}_2$

  $\begin{array}{l}{A}_1=\frac{1}{2}{b}_{1}h\\ A_2=\frac{1}{2}{b}_{2}h\end{array}$

Now we know that median is $M=\frac{b_1+b_2}{2}(i)$

Thus

Total area of trapezoid

  $\begin{array}{l}A=A_1+A_2\\ A=\frac{1}{2}{b}_{1}h+\frac{1}{2}{b}_{2}h\\ A=\frac{1}{2}h(b_1+b_2)\\ A=h\times \left(\frac{b_1+b_2}{2}\right)from(i)\\ A=height\times median\end{array}$

Hence proved.