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

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Math Expert
Joined: 02 Sep 2009
Posts: 51121
In trapezoid ABCE, pictured above, line segment AB has a length of 5,  [#permalink]

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10 Apr 2018, 20:43
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Difficulty:

5% (low)

Question Stats:

92% (01:03) correct 8% (01:06) wrong based on 54 sessions

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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

Attachment:

TrapezoidABCE.png [ 3.55 KiB | Viewed 534 times ]

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

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10 Apr 2018, 21:13
1
[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
Attachments

trap.PNG [ 7.02 KiB | Viewed 461 times ]

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In trapezoid ABCE, pictured above, line segment AB has a length of 5, &nbs [#permalink] 10 Apr 2018, 21:13
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