Question

An architect builds a regular hexagonal patio on a circular garden. The area not covered by the patio will be covered in grass. The radius of the garden is 1.5 meter. Find the area covered by the grass in the garden.

Answer 1

area covered by grass in the garden = 1.24 m²

Explanation:

area of circular garden = πr²

where radius, r = 1.5 m

= 3.14 * (1.5)²

= 3.14 * 2.25 = 7.07 m²

area of hexagonal patio = 3√3/2 * a²

where a is the side of hexagon and will be equal to the radius of the garden, i.e. a = r = 1.5

area of hexagonal patio = 3√3/2 * (1.5)²

= 3 * 1.73 / 2 * 2.25

= 2.59 * 2.25

= 5.83 m²

area covered by the grass = 7.07 - 5.83

= 1.24 m²