Plug in the given area and formula in an equation:
area of equiangular AOB = (s^2 sqrt (3)) / 4
100 sqrt (3) = (s^2 sqrt (3)) / 4
Solve for s to get the radius of the circle:
4*(100 sqrt (3) ) = s^2 sqrt (3)
400 sqrt (3) = s^2 sqrt (3)
Since we have sqrt (3) at both sides, cancel those:
400 = s^2
20cm = s
We can use s as a value for our radius since it is shown that from side AO or OB that it is the radius of the circle.
We now have to use the formula for the area of sector:
area of sector = (angle/360) x pi x r^2
We have a radius (20) and an angle of 60 degrees.
Explanation why it is 60 degrees: The given triangle is an equiangular triangle with same angles in the triangle. The sum of internal angles in a triangle is 180 so, 180 divided by 3 is 60.
Substitute, angle (60°) and radius (20cm) to the formula:
60/360 x pi x (20^2)
= 200/3 pi or 209.44 cm^2
Now subtract the area of the sector to the given area of equiangular triangle to determine the area of the shaded part:
Answers & Comments
Answer:
36.23 cm^2
Step-by-step explanation:
Plug in the given area and formula in an equation:
area of equiangular AOB = (s^2 sqrt (3)) / 4
100 sqrt (3) = (s^2 sqrt (3)) / 4
Solve for s to get the radius of the circle:
4*(100 sqrt (3) ) = s^2 sqrt (3)
400 sqrt (3) = s^2 sqrt (3)
Since we have sqrt (3) at both sides, cancel those:
400 = s^2
20cm = s
We can use s as a value for our radius since it is shown that from side AO or OB that it is the radius of the circle.
We now have to use the formula for the area of sector:
area of sector = (angle/360) x pi x r^2
We have a radius (20) and an angle of 60 degrees.
Explanation why it is 60 degrees: The given triangle is an equiangular triangle with same angles in the triangle. The sum of internal angles in a triangle is 180 so, 180 divided by 3 is 60.
Substitute, angle (60°) and radius (20cm) to the formula:
60/360 x pi x (20^2)
= 200/3 pi or 209.44 cm^2
Now subtract the area of the sector to the given area of equiangular triangle to determine the area of the shaded part:
200/3 pi - 100 sqrt (3) = 36.2344 cm^2