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Anastaziya [24]
3 years ago
15

AREA ADDITION AND SUBTRACTION ASSISTANCE?

Mathematics
1 answer:
Tom [10]3 years ago
7 0

The shaded area is a segment. The area of a segment is

A_{segment}=A_{sector}-A_{triangle}.

You know radius that is the side of isosceles triangle and measure of angle between two equal triangle sides, then

A_{triangle} =\dfrac{1}{2} a\cdot a \sin \alpha=\dfrac{1}{2} 18.6\cdot 18.6 \cdot  \sin 123^{\circ}=172.98\cdot  \sin 123^{\circ}=145.07 sq. m..

The area of sector is A_{sector}=\dfrac{r^2\cdot \alpha}{2}= \dfrac{(18.6)^2\cdot 0.68\pi}{2}=117.63\pi=369.53 sq. m..

Then A_{segment}=369.53-145.07=224.46 sq. m.

Answer: A_{segment}=224.46 sq. m.

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