SOLUTION: The area of a trapezoid is 3350 cm^2, its height is 36.0cm and one of the bases is 45.0cm long. Find the length of the other base.

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Question 191189: The area of a trapezoid is 3350 cm^2, its height is 36.0cm and one of the bases is 45.0cm long. Find the length of the other base.
Answer by ejazali_syed(7) (Show Source):
You can put this solution on YOUR website!
Q) The area of a trapezoid is 3350 cm^2, its height is 36.0cm and one of the bases is 45.0cm long. Find the length of the other base.
A)
I expect you to have internet. Have a look at the picture of trapezoid.
http://upload.wikimedia.org/wikipedia/commons/1/11/Trapezoid.svg
the formula to find the area of a trapezoid is
A = h(a + b)/2 where h is the height of the trapezoid
a and b are the bases of the trapezoid
3350 = 36(45 + b)/2 ==> 6700/36 = b + 45 ==> b = 186.11 - 45
hence b = 141.11cm.
Wonder how the formula for trapezoid is derived??!!!
let me solve it.
The trapezoid can be divided into two triangles and a rectangle.

So from the above figure let the base b be the sum of a and b1 and b2.

________________________
--b1--|--------a--------|--b2--

assume this to be base b which is equal to b1 + a + b2.

so the area of the trapezoid would be the sum of the area of triangle to the left and the area of the triangle to the right and the area of the rectangle with side a and h.
I cant draw the figure here...so try to figure out using my analogy and the above line.

Area = (1/2)(b1)h + a.h + (1/2)(b2)h
= h(a + (b1 + b2)/2)
b = b1 + a + b2 ==> b-a = b1 + b2
Area = h( a + (b-a)/2)
= h(a + b)/2