Geometrical Question?

Question

Parallelogram ABCD is made up of four equilateral triangles of side length. 1. Determine the length of diagonal AC

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Answer 1

An equilateral triangle of side length s has altitude s√3/2.
Thus, the height of the parallelogram is h = √3/2, while the length of the base is b = 2.

If d is the diagonal then
d² = h² + (b + 1/2)² = 3/4 + (5/2)² = 3/4 + 25/4 = 7
Therefore,
d = √7