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D, E, F are the mid points of the sides

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by patanjali.purpose » Mon Apr 09, 2012 9:35 am
D, E, F are the mid points of the sides AB, BC and CA of triangle ABC respectively. What is
the area of DEF in square centimeters?

1) AD = 1 cm, DF = 1 cm and perimeter of DEF = 3 cm
2)Perimeter of ABC = 6 cm, AB = 2 cm, and AC = 2 cm.

OA - D
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by Jim@StratusPrep » Mon Apr 09, 2012 9:49 am
When you have a triangle that connects the midpoints of the sides of a larger triangle, 4 identical triangles are created inside. Thus, all you need are the dimensions to be able to figure out the area. Both statements give you these dimensions.
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by ronnie1985 » Mon Apr 09, 2012 10:55 am
S1. AD = 1 => AB = 2 => EF = 1
DF = 1 and Perimeter DEF = 3 => DE = 1, hence area of the triangle can be calculated Sufficient

S2. AB = 2, AC = 2 => BC = 2 as Perimeter of ABC is given, so we can also find the sides of DEF. Sufficient

(D) is answer
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