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the figure attached?

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by sanju09 » Thu Mar 04, 2010 1:44 am
What is the area of the shaded region in the figure attached?
(A) 72
(B) 57
(C) 55
(D) 54 ½
(E) 51
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by kstv » Thu Mar 04, 2010 1:58 am
IMO B
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by fibbonnaci » Thu Mar 04, 2010 2:40 am
the total area of the rectangle is 8*9= 72.
To find the area of the shaded region, we need to subtract the unshaded region from the total area.
The best way to find the area of the unshaded region is to divide the area in terms of known geometrical figures.
The unshaded region can be divided into a rectangle and a right angled triangle.
the area of the rectangle => 4 * 3 => 12
the area of the right angled triangle is 1/2 * 2 * 3 => 3
The total area of the unshaded region is 15.

The area of shaded region is 72- 15 => 57

IMO B
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by AtifS » Fri Mar 05, 2010 5:47 am
fibbonnaci wrote:the total area of the rectangle is 8*9= 72.
To find the area of the shaded region, we need to subtract the unshaded region from the total area.
The best way to find the area of the unshaded region is to divide the area in terms of known geometrical figures.
The unshaded region can be divided into a rectangle and a right angled triangle.
the area of the rectangle => 4 * 3 => 12
the area of the right angled triangle is 1/2 * 2 * 3 => 3
The total area of the unshaded region is 15.

The area of shaded region is 72- 15 => 57

IMO B
Nice explanation! I had same solution :) but as it's been clearly explained already so don't need to write explanation.
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by hooliganpete » Fri Mar 05, 2010 3:17 pm
We also know that for a four-sided polygon where Base 1 is parallel to Base 2 the formula for the area is equal to:

Base1+Base2*h.
2

In this case, Base 1 = 4, Base 2 = 2, and h = 3. Thus ((2+4)/2)*3 = 9

48+9=57

Answer is B
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by vzzai » Fri Mar 05, 2010 8:54 pm
When should someone imagine that the diagram is drawn to scale and when it is not!? Though, I could solve this. I was still wondering whether it is drawn to scale!? and started digging deepeer in to Coordinate Geometry. Please clarify.
Thank you,
Vj
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by sanju09 » Sat Mar 06, 2010 1:51 am
vzzai wrote:When should someone imagine that the diagram is drawn to scale and when it is not!? Though, I could solve this. I was still wondering whether it is drawn to scale!? and started digging deepeer in to Coordinate Geometry. Please clarify.
A rectangular coordinate system with markings is itself a set of scales. Any line segment shown slanted there is in fact slanted. However, for other questions on GMAT those include a diagram; enough information is revealed through the diagram plus the stem that no ambiguity ever remains.

No imaginations on GMAT please.
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