ABCD is a parallelogram. G is the midpoint of AD and F is the midpoint of AG. The area of the parallellogram ABCD is 200cmsquared. Find the area of the quadrilateral BCGF

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- Oct 8th 2008, 02:59 AM #1

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- Oct 8th 2008, 03:52 AM #2

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Let x = AD

So, AF = x/4

And, DG = x/2

Let h = altitude of the parallelogram where BC and AD are the bases.

So, x*h = 200 sq.cm

Area of any triangle = (1/2)(base)(altitude)

The triangle ABF:

base = AF = x/4

altitude = h also

So, area = (1/2)(x/4)(h) = (1/8)(hx) = (1/8)(200) = 25 sq.cm

The triangle CDG:

base = DG = x/2

altitude = h also

So, area = (1/2)(x/2)(h) = (1/4)(hx) = (1/4)(200) = 50 sq.cm

Therefore,

area of BCGF = 200 -50 -25 = 125 sq.cm -------answer.