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Morgarella [4.7K]
3 years ago
15

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

Mathematics
2 answers:
BigorU [14]3 years ago
8 0
Ratio = A_ABC / A_BDCA = r^2/2 / 3/4(π)r^2 = 4 / 6π = 2 / 3π = 0.21 
Lera25 [3.4K]3 years ago
6 0

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...

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