What is the formula for the area of a circle?

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Ответ:

emilyturchon

10.01.2021

Mathematics

The area of shaded region is 226.4 meter squared.

Step-by-step explanation:

Radius of the circle = r =18.6 m

Angle subtended by chord $\theta = 123^o$

Area of sector = $\frac{\theta }{360^o}\pi r^2$

In ΔOAB

∠A+∠B+∠O= 180°

2∠A+123°= 180°(∠A=∠B, isosceles triangle)

∠A=∠B=28.5°

AC=BC (Radius of the circle bisects the chord at right angle.)...(1)

In ΔOAC

$\sin 123^0=\frac{OC}{OA}$

OC = 8.87 m

$\cos 123^0=\frac{AC}{OA}$

AC = 16.34 m

AB = AC+AB=16.34 m+16.34 m=32.68 m (from (1))

Area of the ΔOAB = $\frac{1}{2}\times OC\times AB$

= $\frac{1}{2}\times 8.87 m\times 32.68 m=144.93 m^2$

Area of segment = Area of sector - Area of triangle:

$371.34 m^2-144.93 m^2=226.41 m^2\approx 226.4 m^2$

The area of shaded region is 226.4 meter squared.

Find area of shaded region. round to the nearest tenth need asap

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