The formula to calculate the area of the shaded piece(A) is,
[tex]Area\text{ of shaded portion = }Area\text{ of the sector - Area of the triangle}[/tex]
The formula for the area of the sector(A1) is,
[tex]A_1=\frac{\theta}{360^0}\times\pi r^2[/tex]
Given
[tex]\begin{gathered} \theta=90^0 \\ r=radius=4m \end{gathered}[/tex]
Therefore,
[tex]\begin{gathered} A_1=\frac{90^0}{360^0}\times\pi\text{\lparen4\rparen}^2=4\pi \\ \therefore A_1=4\pi m^2 \end{gathered}[/tex]
The formula for the area (A2) of the triangle is,
[tex]A_2=\frac{1}{2}absin\theta[/tex]
Given
[tex]\begin{gathered} a=4m \\ b=4m \\ \theta\text{=90}^0 \end{gathered}[/tex]
Therefore,
[tex]\begin{gathered} A_2=\frac{1}{2}\times4\times4\times sin90^0=8sin90^0=8 \\ A_2=8 \end{gathered}[/tex]
Therefore, the area of the shaded piece(A) is
[tex]A=4\pi m^2-8m^2=4\left(\pi-2\right)m^2[/tex]
Hence, the answer is
[tex]4\left(\pi -2\right)m^2[/tex]
