kop wrote:A square ABCD is drawn and point E is marked on AB such that AE=AB/3. Similarly points F, G and H are marked on the sides of the square such that BF=BC/3, CG=CD/3 and DH=DA/3. If the points E, F, G, and H are connected to make a parallelogram, what is the ratio of the area of square ABCD to the area of parallelogram EFGH?
81/16
9/4
9/5
5/4
4/5
PLUG IN an easy figure that satisfies all of the given constraints:
Square ABCD:
Area = s² = 3² = 9.
∆AEH, ∆BEF, ∆CFG, and ∆DGH:
Area of each triangle = (1/2)bh = (1/2)*2*1 = 1.
Combined area of the 4 triangles = 4*1 = 4.
EFGH:
Area = (square ABCD) - (combined area of the 4 triangles) = 9-4 = 5.
Resulting ratio:
ABCD/EFGH = 9/5.
The correct answer is
C.
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