[quote="Bunuel"]

In trapezoid ABCE, pictured above, line segment AB has a length of 5, line segment BC has a length of 5, and line segment CD has a length of 3. What is the area of trapezoid ABCE?

A. 26

B. 27.5

C. 30

D. 32.5

E. 34

Ans: A

Area of trapezoid = \(\frac{(a+b)}{2}\)*h

a,b are length of parallel side.

h=height

a=5, b= 5+3 =8

Now we have to find h,There are some right-angled triangles where all three sides are whole numbers,these triangles are called Pythagorean Triangles. The three whole number side-lengths are called a Pythagorean triple or triad.

An example of Pythagorean triple or triad is a = 3, b = 4 and c = 5,such triangle is called "the 3-4-5 triangle". We can check it as follows:

\(3^2+4^2\) = \(9 + 16 = 25\)so \(a^2 + b^2 = c^2.\)

as 3,4,5 is a Pythagorean triple or triad.

so h will be 4.

Using a=5,b=8 and h= 4 in area formula, we get area of trapezoid as 26

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