Question

Please help me( ´人` )

Answer 1

Answer:

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Step-by-step explanation:

First let's list down the formulas we will be using.

Area of Quadrant = 1/4 x Area of Circle

= $\frac{1}{4} \pi r^{2}$

Area of Part of a circle = (θ/360)$\pi r^{2}$

First, we will find Angle QOT.

Angle QOT = 360 - 231 = 129

Area of ORST = $\frac{129}{360} \pi (21)^{2} \\=\frac{6321}{40} \pi cm^{2}$

Next we know that, Q is midpoint of OR, therefore OQ = QR

and OQ = 0.5 * OR

OQ = 0.5 * 21 = 10.5cm = radius of Quadrant QOP

Area of Quadrant QOP = $\frac{1}{4} \pi (10.5)^{2} \\=\frac{441}{16} \pi cm^{2}$

Lastly,

Area of Shaded Region = Area of ORST - Area of Quadrant QOP

= $\frac{6321}{40} \pi -\frac{441}{16} \pi \\= 409.86cm^{2}$

Similar to the other question you asked, choose the closes answer as there might be some rounding differences. I kept it in fractions as it will ensure maximum precision.