I have a math question for anyone who is good at geometry. I will be very grateful to the solver.?

Question

When their favorite pizza parlor closed, a family went to a new restaurant that served only hexagonal pizzas. The hexagonal pizzas are sold according to their widest diameters. An 18-inch circular pizza used to suffice. To the nearest inch, what size pizza must they buy to have the same amount of pizza?

Answer 1

area of circular pizza = pi x radius squared = pi x 9 squared = pi x 81

area of hexagonal pizza = radius squared x 3 x sin (pi / 3)

so for the two areas to be the same:

pi x 81 = radius squared x 3 x sin (pi / 3)

radius squared = (pi x 81) / (3 x sin (pi / 3)

radius = square root ((27 x pi) / sin (pi / 3))

radius = 9.69 inches

diameter = 19.58 inches

(You would be wise to check ALL the arithmetic -- I was in a hurry.)

Answer 2

Area of an 18inch circular pizza is:
A = π × 9² ≈ 254.47 square inches.
The area of a hexagon pizza with side x is just 6 equalateral triangles so:
A = 3√3/2x² = 2.598x²
So x² = 254.47 / 2.598
x² = 97.945
x = 9.9
So a 10 inch hexagonal pizza is required.