Answer: 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
