Question

Write an expression in terms of pie that represents the area of the shaded part of N

Answer 1

Let us write the formula for the area of the shaded portion,

`\text{Area of a }\sec tor\text{=}(\theta)/(360)*\pi r^2`
`\begin{gathered} \text{where }\theta=360^0-75^0=285^0 \\ r=\text{radius}=x \end{gathered}`

Let us now solve for the area in terms of π,

`\begin{gathered} \text{Area of the sector=}\frac{\text{285}^0}{360^0}*\pi* x^2 \\ =(19)/(24)x^2\pi \\ =0.7917x^2\pi\approx0.79x^2\pi\text{ (to nearest hundredth)} \end{gathered}`

Hence, the area in terms of π is 0.79x²π units.