Chapter 11.3, Problem 7CE

(a)

To determine

To Find: What special quadrilateral is formed if the congruent trapezoids shown are slid together?

Answer to Problem 7CE

Parallelogram

Explanation of Solution

Given:

  

When the congruent trapezoids shown are slid together it will become a parallelogram.

Since both trapezoids are congruent they have an equal area.

And the opposite sides are equal and congruent

Thus it will become a parallelogram.

(a)

To determine

To Derive: The formula.

Explanation of Solution

Given: $A=\frac{1}{2}h(b_1+b_{2)}$

  

Area of parallelogram

  $A=bh$

Here

When we join both trapezoids

Base of parallelogram = $b_1+b_2$

i.e.

Area of parallelogram

  $A=(b_1+b_2)h\mathrm{....}(i)$

Now both the trapezoid are congruent thus they have an equal area

i.e.

  $\begin{array}{l}A+A=(b_1+b_2)h\\ 2A=(b_1+b_2)h\\ A=\frac{1}{2}(b_1+b_2)h\end{array}$

Hence proved.