Can you show that you can work out the area of a regular hexagon with a perimeter of LX inches rounding your answer to a suitable degree of accuracy?

Answer 1

Perimeter in inches = LX = 60. A regular hexagon with a perimeter of 60 inches has 6 equal sides of 10 inches. A regular hexagon has 6 equal interior equilateral triangles So in order to find the area of the hexagon we must first find the area of one of its interior triangles and then multiply the result by 6. Area of a triangle = base times perpendicular height divided by 2. An equilateral triangle can be considered as being two right angled triangles joined together. So by halving the length of its base we can find its perpendicular height by using Pythagoras' Theorem: hypotenuse2-base2 = perpendicular height2. 102-52 = 75 square inches. Square root of 75 = 8.660254038 inches. Area of the equilateral triangle = 10*8.660254038/2 = 43.30127019 square inches. Area of the regular hexagon = 43.30127019*6 = 259.8076211 square inches. Therefore the area of a regular hexagon with a perimeter of 60 inches is 260 square inches which is correct to 3 significant figures.