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alukav5142 [94]
3 years ago
6

Find area of shaded region. Round to the nearest tenth need help ASAP

Mathematics
2 answers:
Kryger [21]3 years ago
8 0

Answer:

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.

Serjik [45]3 years ago
5 0

the answer for the shaded region is 320.59 m² or approximately 321 m². applying area of circle, unitary method, sin law and area of triangle using semi perimeter.

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