Question

Please help me find the area of the shaded piece in pi form. Question 4

Answer 1

The formula to calculate the area of the shaded piece(A) is,

`Area\text{ of shaded portion = }Area\text{ of the sector - Area of the triangle}`

The formula for the area of the sector(A1) is,

`A_1=(\theta)/(360^0)*\pi r^2`

Given

`\begin{gathered} \theta=90^0 \\ r=radius=4m \end{gathered}`

Therefore,

`\begin{gathered} A_1=(90^0)/(360^0)*\pi\text{\lparen4\rparen}^2=4\pi \\ \therefore A_1=4\pi m^2 \end{gathered}`

The formula for the area (A2) of the triangle is,

`A_2=(1)/(2)absin\theta`

Given

`\begin{gathered} a=4m \\ b=4m \\ \theta\text{=90}^0 \end{gathered}`

Therefore,

`\begin{gathered} A_2=(1)/(2)*4*4* sin90^0=8sin90^0=8 \\ A_2=8 \end{gathered}`

Therefore, the area of the shaded piece(A) is

`A=4\pi m^2-8m^2=4\left(\pi-2\right)m^2`

Hence, the answer is

`4\left(\pi -2\right)m^2`