Find the area of the shaded sector. Round to the nearest hundredths place.
SR= 26 m

315.45 m^2

Step-by-step explanation:

We know that the area of a circle is written as:

A = pi*R^2

Where:

pi = 3.14

R = radius of the circle.

In this case, we know that SR (the diameter) is equal to 26m

And the radius is half of the diameter, then:

R = 26m/2 = 13m

Now, in the image we can see that we have half of the circle shaded, the area of that part will be equal to half the area of a complete circle, then the area of that part is:

A = (1/2)*3.14*(13m)^2 = 265.33 m^2

We also can see that we have a small arc shaded.

The area of a given arc of an angle θ, is given by:

A = (pi*R^2)*(θ/360°)

Now we want to find the angle of this arc, that is the angle:

∠PQ

We know that:

∠SR = 180°   (this is a straight line)

∠RQ = 73°

and i assume that:

∠PS = 73°

if we look at the image, we can see that we must have:

∠QR + ∠PQ + ∠SP = ∠SR

73° + ∠PQ  + 73° = 180°

∠PQ = 180° - 2*73° = 34°

Then the area of the small arc is:

A' = (3.14*(13m)^2)*(34°/360°) = 50.12 m^2

The total shaded area is equal to the sum of the two areas we calculated, this is:

Total area = A + A' = 265.33 m^2 + 50.12 m^2 = 315.45 m^2

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