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Re: What is the area of the shaded figure? [#permalink]
04 Jun 2012, 04:43

1

This post received KUDOS

Hi,

The figure can be split into two triangles: tri(ABE) & tri(DCE)

Assuming CE=DE=x(since angle C = 45) CD = \sqrt{2}x = \sqrt{2} + \sqrt{2}/2 or x =3/2

area(DCE) = (1/2)*x^2=1/2*3/2*3/2=9/8

Now, in tri(ABE) AE = AD-x=\sqrt{3}/2 ratio of sides opposite to angles 30:60:90=1:\sqrt{3}:2 Thus, BE=1/2 area(ABE)=1/2*AE*BE=1/2*\sqrt{3}/2*1/2=\sqrt{3}/8

area of the figure = area(ABE)+area(DCE)=(9+\sqrt{3})/8

Re: What is the area of the shaded figure? [#permalink]
24 Aug 2009, 11:36

My answer is A.

I split the graph in two right triangles. One triangle with angles 45-45-90, another with angles 60-30-90.

In triangle, 45-45-90, the length of the sides are in ratio 1:1:2^(1/2) In triangle, 30-60-90, the length of the sides are in ratio 1:3^(1/2):2. Using this I figured out area of each triangle and then the total.

Re: What is the area of the shaded figure? [#permalink]
24 Aug 2009, 21:03

LenaA wrote:

My answer is A.

I split the graph in two right triangles. One triangle with angles 45-45-90, another with angles 60-30-90.

In triangle, 45-45-90, the length of the sides are in ratio 1:1:2^(1/2) In triangle, 30-60-90, the length of the sides are in ratio 1:3^(1/2):2. Using this I figured out area of each triangle and then the total.

Quite Right LenaA! A it is.
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Re: What is the area of the shaded figure? [#permalink]
14 Nov 2013, 11:34

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Re: What is the area of the shaded figure? [#permalink]
31 Jan 2014, 08:20

mendelay wrote:

What is the area of the shaded figure?

Nice question we need to know both triangles thr 45-45-90 and 30-60-90, these are a MUST

Now the first triangle is the 45-45-90 so the hipothenuse is sqrt (2) + sqrt (2)/2

Therefore the side is 3/2 and area is 9/8

Now for the second triangle we need to subtract 3/2 from (3+sqrt (3)/2) and we get that the side opposite to 60 degrees is sqrt 3/2). Therefore side is 1/2 and area is sqrt (3) /8

So total area is sum of both or 9+ sqrt (3) / 8

Answer is A

Hope it helps Cheers J

gmatclubot

Re: What is the area of the shaded figure?
[#permalink]
31 Jan 2014, 08:20