Question

A sector with a radius of \maroonD{10\,\text{cm}}10cmstart color #ca337c, 10, start text, c, m, end text, end color #ca337c has a central angle measure of \purpleD{252\degree}252°start color #7854ab, 252, degree, end color #7854ab.

Answer 1

Given: A sector with

`\begin{gathered} radius=10cm \\ sectorangle(\theta)=252^0 \end{gathered}`

To Determine: The area of the sector

Solution

The area of a sector is given as

`\begin{gathered} AS=(\theta)/(360^0)*\pi r^2 \\ AS=Area\text{ of sector} \end{gathered}`

Substitute the given into the formula

`\begin{gathered} AS=(252)/(360)*\pi*10^2 \\ AS=0.7*100\pi \\ AS=70\pi cm^2 \\ AS=219.91cm^2 \end{gathered}`

Hence, the area of the sector is 70πcm² or 219.91cm^2