Question

The lengths, in order, of four consecutive sides of an equiangular hexagon are 1, 7, 2 and 4 units, respectively. What is the sum of the lengths of the two remaining sides?

Answer 1

9

Explanation:

Extend every other side of the hexagon so that a triangle is formed. Since the hexagon is equiangular, the overall triangle is an equilateral triangle, as well as the smaller triangles in the corners.

The length of the sides of the overall triangle is 7 + 2 + 4 = 13.

Therefore, the other two sides of the hexagon are 5 and 4.

The sum is 5 + 4 = 9.