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# If AB = BC, which of the following is an expression for the

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If AB = BC, which of the following is an expression for the [#permalink]  24 May 2017, 02:31
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Question Stats:

90% (01:50) correct 9% (01:05) wrong based on 11 sessions

If AB = BC, which of the following is an expression for the area of quadrilateral ABDE ?

A) $$\frac{a^2}{2} - \frac{b^2}{2}$$

B) $$\frac{a^2}{2} + \frac{b^2}{2}$$

C) $$a^2 - b^2$$

D)$$\frac{a^2}{4} - \frac{ab}{2}$$

E) $$\frac{a^2}{4} + \frac{ab}{2}$$
[Reveal] Spoiler: OA

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Re: If AB = BC, which of the following is an expression for the [#permalink]  24 May 2017, 13:23
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Expert's post
Carcass wrote:

If AB = BC, which of the following is an expression for the area of quadrilateral ABDE ?

A) $$\frac{a^2}{2} - \frac{b^2}{2}$$

B) $$\frac{a^2}{2} + \frac{b^2}{2}$$

C) $$a^2 - b^2$$

D)$$\frac{a^2}{4} - \frac{ab}{2}$$

E) $$\frac{a^2}{4} + \frac{ab}{2}$$

Area of quadrilateral ABDE = (Area of ∆ABC) - (Area of ∆EDC)
So, what are the areas of each triangle?

Area of ∆ABC
Since AB = BC, then side BC also has length a (Aside: ∆ABC is called an isosceles right triangle)
Since ∆ABC is a right triangle, we can make one of the legs the base (with length a) which makes the other leg the height (height = a)
Area of triangle = (base)(height)/2
So, the area of ∆ABC = (a)(a)/2 = a²/2

Area of ∆EDC
We must first recognize that ∆ABC and ∆EDC are SIMILAR TRIANGLES
This means that ∆EDC is also an isosceles right triangle
In this case, the base and the height are both equal to b.
So, the area of ∆EDC = (b)(b)/2 = b²/2

So, area of quadrilateral ABDE = a²/2 - b²/2
= (a² - b²)/2

[Reveal] Spoiler:
A

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com

Re: If AB = BC, which of the following is an expression for the   [#permalink] 24 May 2017, 13:23
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