Question

what is the area of a sector bounded by a 135 degree arc? what would the answer be with the pi symbol next to it ?

Answer 1

The formula for area of a sector, A, is given below as,

`\text{Area of a sector, A =}(\theta)/(360^0)*\pi r^2`

Where,

`\begin{gathered} r\text{ is the radius} \\ \theta\text{ is the angle subtended by the arc} \\ r=4\text{ miles} \\ \theta=135^0 \\ \pi=3.14 \end{gathered}`

Substituting the variables into the formula for the area of a sector given above,

`\begin{gathered} A=(\theta)/(360^0)*\pi r^2 \\ \Rightarrow(135^0)/(360^0)*3.14**(4)^2=18.84mi^2 \end{gathered}`

The simplest form of the area of the sector, A, is 18.8mi² (one decimal palce).