Question

Simon says that to find the area of a trapezoid, you can multiply the height by the top base and the height by the bottom base. Then add the two products together and divide the sum by 2. Is Simon correct? Complete the explanation.

Answer 1

Yes, Simon is correct.

Explanation:

A trapezoid refers to a quadrilateral that is convex in shape; as such it has no equal sides and no parallel sides.

Let the height of a trapezoid be h.

Let the top base of a trapezoid be b1.

Let the bottom base of a trapezoid be b2.

`Area \; of \; trapezoid = \frac {1}{2} * (Sum \; of \; nonparallel \; sides) * height`

Therefore,
`Area \; of \; trapezoid = \frac {1}{2} * (b_(1) + b_(2)) * h`

`Area \; of \; trapezoid = \frac {1}{2} * (b_(1)h + b_(2)h)`

`Area \; of \; trapezoid = \frac {b_(1)h + b_(2)h}{2}`

Hence, to find the area of a trapezoid, you will multiply the height by the top base and the height by the bottom base. Then you add the two products together and divide the sum by 2.