Question

Determine the height of a trapezoid given that the area is 57 in², and the bases are 12 in and 4 in.​

Answer 1

`7.125\;in`

Explanation:

Area of a trapezoid is given by

`A=\frac{(a+b)h}2}`

where

A = area (57)

a, b are the two bases (4 and 12)

h the height

Multiplying both sides by 2 yields

`2A = (a+b)h`

Dividing both sides by (a+b) gives

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

or

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

Plugging in given values for A = 57, a=4 and b=12 gives

`h = (2(57))/(4+12) = (114)/(16) = 7.125\;in`