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 1First, let us state the formula for calculating the area of a trapezoid:
A = (
a +
b)/2 X
hWhere
A = area of the trapezoid,
a = length of AB,
b = length of CD, and
h = distance between AB and CD.
STEP 2Substitute 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 3Let'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 =
9.875cmCD = AB + 8
CD =
17.875cm