Explanation
We must compute the area of the yellow triangle of the diagram:
The area of the yellow portion is given by:
[tex]A_Y=A_{CS}-A_{BT.}[/tex]
Where:
• Ay = is the area of the yellow portion,
,
• Acs = is the area of the circular sector with angle θ,
,
• Abt = is the area of the blank triangle inside the circular sector of angle θ.
1) Area of the circular sector with angle θ
First, the angle of this circular sector is given by:
[tex]θ=360°-270°=90°.[/tex]
The radius of the circular sector is r = 5 m.
The area of the circular sector is given by:
[tex]A_{SC}(θ)=\pi r^2\times\frac{θ}{360°}.[/tex]
Replacing the values of θ and r, we get:
[tex]A_{SC}(\theta=90°)\cong3.14\cdot(5m)^2\times(\frac{90°}{360°})=19.625m^2.[/tex]
2) Area of the blank triangle
We see that the blank triangle is a right isosceles triangle with cathetus:
• b = base = 5m,
,
• h = height = 5m.
The area of this triangle is given by:
[tex]A_{BT}=\frac{1}{2}\cdot b\cdot h=\frac{1}{2}\cdot(5m)\cdot(5m)=12.5m^2.[/tex]
3) Area of the yellow portion
Replacing the values found above in the equation of the yellow portion, we get:
[tex]A_Y\cong19.625m^2-12.5m^2=7.125m^2.[/tex]Answer
The area of the yellow portion is approximately 7.125 m².
