Area of Trapezium

by Oshi
(Dubai)

Question

ABCD is a trapezium of area 91cm2. CD is parallel to AB and CD is longer than AB by 8cm. If the distance between AB and CD is 7cm, find AB CD.

Answer

STEP 1
First, let us state the formula for calculating the area of a trapezoid:

A = (a + b)/2 X h

Where A = area of the trapezoid, a = length of AB, b = length of CD, and h = distance between AB and CD.

STEP 2
Substitute the values we have into the formula:

91 = (AB + CD)/2 X 8

Knowing that CD is longer than AB by 8cm, we could include that information in the equation like this:

91 = (AB + (AB + 8))/2 X 8

STEP 3
Let's solve the equation!

91 = (2AB + 8)/2 X 8
91 = (AB + 4) X 8
91 = 8AB + 32
91 - 32 = 8AB
79 = 8AB
AB = 79/8
AB = 9.875cm
CD = AB + 8
CD = 17.875cm