Question

A package designer wants the hexagonal base of a hat box to have an area of

about 200 in.2. About how long is each side?

Answer 1

About 9inches long

Explanation:

Area of a hexagon = 3√3/2 a²

a is the length of each side

Given

Area of the hexagon = 200in²

Substitute

200 = 3√3/2 a²

200×2 = 3√3 a²

400 = 3√3a²

a² = 400/3√3

a² = 400/5.196

a² = 76.982

a = √76.982

a = 8.774

Hence the length of each side is about 9inches long (to nearest inches)