Question

"What is the ratio of the area of TRIANGLE ABC to the area of sector BDCA (the sector spanned by arc BDC)?

"

Answer 1

ratio = A_ABC / A_BDCA = r^2/2 / 3/4(π)r^2 = 4 / 6π = 2 / 3π = 0.21 

Answer 2

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 .

$\text{Area of triangle ABC=}\frac{1}{2}\times base\times height$

$=\frac{1}{2}\times r\times r=\frac{1}{2}r^2$

$\text{Area of sector BDCA=}\frac{\theta}{360}\times \pi r^2$

$=\frac{270}{360}\times \pi r^2$

$Ratio=\frac{\text{area of triangle}}{\text{area of sector BDCA}}$

$=\frac{\frac{1}{2}r^2}{\frac{270}{360}\times \pi r^2}=\frac{7}{33}$

$\text{The ratio is }\frac{7}{33}=0.212...$