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How to find the value of a + b + c.

I know the answer but I do not know how to arrive at the answer:

answer = 9

How to find the value of a + b + c. I know the answer but I do not know how to arrive-example-1
User DUDANF
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1 Answer

21 votes
21 votes

The attached picture is of a similar problem. But different radii.

Notice how you can form 2 equilateral triangles, and that there are 4 semi circles (at AC, AD, BC, BD).

This is because points C and D lie on the circumference of the circles. So distance from centres( A and b) to C and D are the radius

To get the area of your shaded section, you would just need to add up the areas of the 4 semi circles and 2 equi. triangles.

To get the area of a semi circle, work out the area of one of the sectors, i.e sector ABC, then subtract area of an equilateral triangle.

(Note, due to symmetry all semi circles have same area)

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For example, for the picture below:

Area of equi triangle = absinC = 1*1*sin60 = √(3) --> (C is angle)

Area of sector = (angle/360) * πr² = (60/360) * π * (1)² = π/6

So area of 1 semi circle = Area of Sector - Area of equi triangle

= π/6 - √(3)

Now you would just add the areas of 4 semi circles, and 2 equi triangles, and compare coefficients to get a, b, c.
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Now you would do the same for your question, except radius is now 6cm instead of 1cm.

How to find the value of a + b + c. I know the answer but I do not know how to arrive-example-1
User Becks
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2.6k points