Answer:
\(\text{The ratio is }\frac{7}{33}=0.212...\)
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 .
\(\text{Area of triangle ABC=}\frac{1}{2}\times base\times height\)
\(=\frac{1}{2}\times r\times r=\frac{1}{2}r^2\)
\(\text{Area of sector BDCA=}\frac{\theta}{360}\times \pi r^2\)
\(=\frac{270}{360}\times \pi r^2\)
\(Ratio=\frac{\text{area of triangle}}{\text{area of sector BDCA}}\)
\(=\frac{\frac{1}{2}r^2}{\frac{270}{360}\times \pi r^2}=\frac{7}{33}\)
\(\text{The ratio is }\frac{7}{33}=0.212...\)
