Answer:
[tex]\text{The ratio is }\frac{7}{33}=0.212...[/tex]
Step-by-step explanation:
Given the circle with radius r
we have to find the ratio of the area of triangle ABC to the area of sector BDCA .
[tex]\text{Area of triangle ABC=}\frac{1}{2}\times base\times height[/tex]
[tex]=\frac{1}{2}\times r\times r=\frac{1}{2}r^2[/tex]
[tex]\text{Area of sector BDCA=}\frac{\theta}{360}\times \pi r^2[/tex]
[tex]=\frac{270}{360}\times \pi r^2[/tex]
[tex]Ratio=\frac{\text{area of triangle}}{\text{area of sector BDCA}}[/tex]
[tex]=\frac{\frac{1}{2}r^2}{\frac{270}{360}\times \pi r^2}=\frac{7}{33}[/tex]
[tex]\text{The ratio is }\frac{7}{33}=0.212...[/tex]
