Find the Area of the shaded region in the given problem

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chwala
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Homework Statement
See attached
Relevant Equations
Circular measure
Wawawawawa boggled me a little bit... but finally managed it...seeking alternative approach guys;

kindly note that what i have indicated as ##*## and a ##√## is the correct working ...

Text book answer indicates ##17.5## as answer... will re check my rounding solutions later...
1678364583516.png


My working- allow me to copy paste here...will later type the working...

1678364659756.png

1678364699766.png
 
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From your sketch, say S is area we want, it seems
[tex]2S=\frac{1}{2}*20^2 (4\alpha)-4*\frac{1}{2}*15\cos \alpha*5-2*\frac{1}{2}*5^2(\pi+2\alpha)[/tex]
where
[tex]\sin\alpha =\frac{1}{3}[/tex]
Is it same as your idea ?
 
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FAQ: Find the Area of the shaded region in the given problem

How do I find the area of the shaded region in a composite shape?

To find the area of the shaded region in a composite shape, break the shape down into simpler geometric figures (like rectangles, triangles, circles, etc.), calculate the area of each individual shape, and then add or subtract these areas as needed to find the area of the shaded portion.

What formulas do I need to know to calculate the area of different shapes?

Common formulas include the area of a rectangle (length × width), the area of a triangle (0.5 × base × height), the area of a circle (π × radius²), and the area of a trapezoid (0.5 × (base1 + base2) × height). Knowing these formulas helps in calculating the area of more complex shapes.

How do I handle irregular shapes when finding the area of the shaded region?

For irregular shapes, try to approximate the area by dividing the shape into a combination of regular shapes whose areas you can calculate. Alternatively, use methods like the grid method, where you count the number of full and partial grid squares that the shape covers.

What if the shaded region is part of a circle or involves sectors of a circle?

When dealing with circular sectors, use the formula for the area of a sector (θ/360 × π × radius²) where θ is the central angle in degrees. For segments, you might need to subtract the area of the triangular portion from the sector area.

How do I find the area of the shaded region if it involves subtracting areas of shapes?

First, calculate the area of the larger shape that encompasses the shaded region. Then, calculate the area of the shape(s) that need to be subtracted. Subtract the area of the smaller shape(s) from the area of the larger shape to find the area of the shaded region.

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