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Printsmc
geometry intermediate
Problem
(A)
(B)
(C)
(D)
(E)
Solution
First, we calculate the area of 1 triangle. For an equilateral triangle with side , its area is . If the side of the equilateral triangle is , the area of one such triangle is . There are 5 equilateral triangles in total, overlapping by an area of 4 smaller equilateral triangles. Each smaller triangle is one fourth as big as the big equilateral triangles. Therefore, we subtract the overlapping area, which is equivalent to the area of 1 big equilateral triangle. Hence, the total area is equal to the area of 4 equilateral triangles, which is .
Final answer
E