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In trapezoid ABCE, pictured above, line segment AB has a length of 5,

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In trapezoid ABCE, pictured above, line segment AB has a length of 5, [#permalink]

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New post 10 Apr 2018, 21:43
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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


[Reveal] Spoiler:
Attachment:
TrapezoidABCE.png
TrapezoidABCE.png [ 3.55 KiB | Viewed 302 times ]
[Reveal] Spoiler: OA

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In trapezoid ABCE, pictured above, line segment AB has a length of 5, [#permalink]

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New post 10 Apr 2018, 22:13
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[quote="Bunuel"]Image

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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In trapezoid ABCE, pictured above, line segment AB has a length of 5,   [#permalink] 10 Apr 2018, 22:13
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