Answer:
1. Area = 113.1 square units
2. Area = 28.27 square units
3. Area of Shaded = 22.27 square units
Explanation:
1.
Area of the circle is given by the formula
where A is the area and r is the radius
In our case the radius is 6 units, thus we have:
Area = 113.1 square units
2.
When we have the angle given in radians, the area of sector is given by the formula
Where
is the central angle ( in our case
and r is the radius (it is 6)
Plugging in these info into the formula we have area of sector:
Area = 28.27 square units
3.
Area of shaded region = Area of Sector - Area of Triangle
We know area of sector is 28.27
Since the angle is 90 degrees, we have a right triangle, we can use the pythagorean theorem to find the height of the triangle, CE.
Thus
The area of triangle is
where b is the base (in our case it is DC = 3 ) and h is the height (in our case it is CE, which is 4). Plugging into the formula we have the area of triangle as:
Area of Shaded = 28.27 - 6 = 22.27 square units