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

`\text{The ratio is }(7)/(33)=0.212...`

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=}(1)/(2)* base* height`

`=(1)/(2)* r* r=(1)/(2)r^2`

`\text{Area of sector BDCA=}(\theta)/(360)* \pi r^2`

`=(270)/(360)* \pi r^2`

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

`=((1)/(2)r^2)/((270)/(360)* \pi r^2)=(7)/(33)`

`\text{The ratio is }(7)/(33)=0.212...`

Answer 2

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