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.)

Answer 1

The area of trpezoid is 48 in²

Explanation:

The altitude is 6 inches and the median is 8 inches.

Median of trapezoid is half of sum of side of parallel side.

Let the length of parallel side be a and b

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

`a+b=2* median`

`a+b=2(8)=16` inches

Altitude (h) = 6 inches

`\text{Area pf trpezoid}=(1)/(2)(\text{sum of parallel side})h`

Area of trpzoid
`=(1)/(2)(16)(6)=48\text{ in}^2`

Hence, The area of trpezoid is 48 in²

Answer 2

We can calculate the area using the formula for the area of trapezoid:
A = (1/2)(b1 + b2)*h
Where (b1+b2)/2 is equal to median as stated in the problem.
Therefore the area is:
A = Median * h
A = 8 * 6
A = 48 square inches