Brent@GMATPrepNow wrote: ↑Tue May 05, 2020 4:33 pm
If ABCDEFGH is a regular octagon, what fraction of the octagon is shaded?
A) 1/12
B) 1/8
C) 1/6
D) 1/4
E) 3/8
Answer:
D
Source:
www.gmatprepnow.com
If we focus on
rectangle BCFG, we might recognize that
the area of the shaded portion is half the area of the rectangle BCFG
How do we know this?
Well, we know that the area of the rectangle =
(base)(height)
And we know that the area of the triangle =
(base)(height)/2
Since both shapes have the
same base and height, it must be the case that
the area of the shaded portion is half the area of the rectangle BCFG
With this in mind, let's divide
rectangle BCFG into TWO EQUAL rectangles.
From here, we can add two smaller triangles.
Since the area of each small triangle is HALF the area of each small rectangle, we can conclude that
the combined areas of the two small triangles is HALF the combined areas of the two small rectangles.
In other words,
the combined area of the two shaded triangles is the same as the area of the original triangle (triangle YGF)
At this point, when we add a couple of extra diagonals to the diagram...
.... we can see that the shaded portions account for 2/8 of the entire octagon.
Since 2/8 = 1/4, the correct answer is D.
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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