Please help me solve this geometry task

Question

Please help me solve and understand this...I would be very grateful...

Jada and Andre want to share a big slice of pizza so that each of them gets the same amount, but Andre doesn’t like the crust. The pizza slice is a sector of a circle with a radius of 20 cm and a central angle that measures  pi/3  radians.

How can Andre and Jada divide the slice of pizza into 2 equal pieces so that Andre doesn’t have to eat any crust?

Answer 1

The total area of the pizza is πr² = π(20)² = 400π cm²

The pizza is cut into 6 slices since π/3 radians (60°) is 1/6 of 2π radians (360°) of a full circle.

So a slice of pizza has an area of 400π/6 cm² = 200π/3 cm²

An equilateral triangle can be cut from the shared pizza slice so that it has half the area of the whole slice. This will be the half slice with no crust for Andre.

An equilateral triangle with side length x has area A_Δ = (1/2)bh = (1/2)(x)((√3/2)x) = (√3/4)x² cm²

Half the area of a pizza slice is (1/2)(200π/3) = 100π/3 cm²

to find length of the side of the equilateral triangle of the half slice with no crust set A_Δ = 100π/3 cm²

A_Δ = (√3/4)x² = 100π/3

x² = 400π/(3√3)

x = √[400π/(3√3)] = √[241.84] = 15.6 cm

answer

Cut a piece for Andre that is an equilateral triangle with side length 15.6 cm.

This piece will have no crust and will be half of the slice that it is cut from.