SOLUTION: In the figure, triangle Δ ABC is an equilateral triangle. The points D and E are the midpoints of sides AC and AB, respectively. What is the ratio of the area of the quadrilateral

Question 1149752: In the figure, triangle Δ ABC is an equilateral triangle. The points D and E are the midpoints of sides AC and AB, respectively. What is the ratio of the area of the quadrilateral DEFG to the area of triangle ABC?
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Answer by ikleyn(52824) (Show Source): You can put this solution on YOUR website!
.


Let the side length of the equilateral triangle ABC is "a".


Then the area of the triangle is  A = .


The length of the base GF of the rectangle  is  b = ;  

its height GD is half of the triangle height     h =  = .


Hence, the area of the rectangle is  B = b*h = .


The ratio under the question   = .    ANSWER

Solved.

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