Question

Find the area of the shaded region.

Answer 1

Answer:

The area of the shaded region is $11.6\ cm^{2}$

Step-by-step explanation:

we know that

The area of the shaded region is equal to the area of the sector of circle of angle 68.9 degrees minus the area of the isosceles triangle

step 1

Find the area of sector of the circle

The area of circle is equal to

$A=\pi r^{2}$

assume

$\pi =3.14$

$r=9.28\ cm$

substitute

$A=(3.14)(9.28)^{2}$

$A=270.41\ cm^{2}$

Remember that the area of a circle subtends a central angle of 360 degrees

so

using proportion Find out the area of a sector with a central angle of 68.90 degrees

Let

x -----> the area of a sector

$270.41/360=x/68.90\\\\x=68.90*270.41/360\\\\x=51.75\ cm^{2}$

step 2

Find the area of the isosceles triangle

Applying the law of sines

The area is equal to

$A=(1/2)r^{2}sin(68.90)$

we have

$r=9.28\ cm$

substitute

$A=(1/2)(9.28)^{2}sin(68.90)=40.17\ cm^{2}$

step 3

Find the area of the shaded region

$51.75-40.17=11.58\ cm^{2}$

Round to the nearest tenth

$11.58=11.6\ cm^{2}$