Question

Find the area of a trapezoid if the altitude is 6 inches and the median is 8 inches. (Hint: Recall that the median of a

trapezoid is equal to half the sum of the bases.)
24 sq units
48 sq. units
96 sq. units

Answer 1

=48 sq. units.

Explanation:

Area of a trapezoid =h× (a+b)/2

(a+b)/2 is the median ( half of the sum of the two parallel sides also called the bases.

Median=8 inches

Altitude is the distance between the two parallel sides= 6 inches

A=6 inches×8 inches

=48 sq. units.

Answer 2

48 sq. units

Explanation:

The area of a trapezoid is given by half sum of the bases multiplied by the height

`=(1)/(2) (a+b)h`

where a and b are the two parallel sides of the trapezoid and h is the height or amplitude of the trapezoid

But you are aware that, the median of a trapezoid is equal to half the sum of the bases, thus the first part of the formulae is covered by the median

`Median=(1)/(2) (a+b)`

Hence area, A, of a trapezoid is simplified to product of median and amplitude

`A=amplitude*median\\\\A=6*8=48sq.units`