practice examination #1

by **reshma_menghani** Fri Sep 21, 2007 4:57 pm

please help
i do not understand how you got 54(3) ^(1/2)

by **reshma_menghani** Fri Sep 21, 2007 4:58 pm

i mean how you get the area of the hexagon...i can't understand how you got the area of the hexagon.

by S Thu Sep 27, 2007 4:01 am

Hexagon = 6 equilateral treingles
So, A(hex) = 6 * sqrt(3)/4 * 6*6 = 54 sqrt (3) .............(1)

Area of inner circle, with radius 3 = pi *3*3 = 9 pi ................(2)

Now area of reagions of circles A - F which is inside hexagon = 6 * (120/360) * pi * 3*3 = 18pi ...............(3)

So, area of shaded region = (1) - (2) - (3) = Choice E

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reshma_menghani Wrote:i mean how you get the area of the hexagon...i can't understand how you got the area of the hexagon.

by **RonPurewal** Tue Oct 02, 2007 5:36 am

Notice the 'split' between the two answer choices here - almost reminiscent of the 'splits' in sentence correction problems. Essentially, you have to choose between 108 and 54*root(3) for the area of the hexagon. If you remember that 30-60-90 and equilateral triangles contain root(3)'s (and you recognize that hexagons involve these sorts of triangles when they're split up), then you've got your answer right there. If that's too nebulous for you, then note (as has the poster above me) that the area of an equilateral triangle is given by the formula root(3)/4 times side squared.