Find the Area of the shaded region in the given problem

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  • #1
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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What is the formula for finding the area of a shaded region?

The formula for finding the area of a shaded region depends on the shape of the region. For example, the formula for finding the area of a circle is A = πr^2, while the formula for finding the area of a rectangle is A = length x width. It is important to identify the shape of the region and use the appropriate formula to find its area.

What information do I need to know to find the area of a shaded region?

To find the area of a shaded region, you will need to know the dimensions of the region. This can include the length, width, radius, or any other necessary measurements. It is also helpful to have a diagram or visual representation of the shaded region to better understand its shape.

Can I use the same formula to find the area of any shaded region?

No, the formula for finding the area of a shaded region will vary depending on the shape of the region. Different shapes require different formulas to find their area. It is important to identify the shape of the region and use the appropriate formula to accurately find its area.

What units should I use when finding the area of a shaded region?

The units used to measure the dimensions of the shaded region should also be used for the area. For example, if the length and width of a rectangle are measured in meters, the area will be measured in square meters. It is important to use consistent units to ensure accurate calculations.

Why is finding the area of a shaded region important?

Finding the area of a shaded region is important in many fields, such as mathematics, science, engineering, and architecture. It allows us to accurately measure and compare the size of different regions, and can also help us solve real-world problems, such as calculating the amount of material needed for a construction project.

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