Find the area of each sector of a circle. leave your answer in terms of pie​

If we have a circle of radius R, the area of the circle is:

A = pi*R^2

And if we have a section of angle θ, the area of the section will be:

A = (θ/360°)*pi*R^2

13) We have a circle of radius R = 2.

We can see that we have a right angle (90°) plus an angle of 45°

Then the total angle of the shaded part is:

θ = 90° + 45° = 135°

Then the area of the shaded part is:

A = (135°/360°)*pi*2^2 = 1.5*pi

14) Here we have a diameter equal to 10 units, and we know that the radius is half of the diameter, then:

R = 10/2 = 5

Always when we divide an angle by a straight line that passes through the center, we create two angles of 180°.

In the image, we can see that the angle of the non-shaded section is 72°

Then the angle of the shaded region must be such that:

θ + 72° = 180°

θ = 180° - 72° = 108°

Then the area of the shaded region is:

A = (108°/360°)*pi*(5)^2 = 7.5*pi

15) Here we have a circle with a diameter of 12 units, then the radius is:

R = 12/2 = 6

And we can use the same reasoning than before for the angle of the shaded region.

We can see that the angle of the non-shaded region is 120° is given by:

θ + 120° = 180°

θ = 180° - 120° = 60°

Then the area of the shaded region is:

A = (60°/360°)*pi*6^2 = 6*pi

5+2x=a

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