Calculate Blue Surface Area of Circles and Rosette

[kristo]

Homework Statement

Find the blue colored surface area.
1 http://img338.imageshack.us/img338/1630/graph1zd7.png
The radii of the circles are 3 cm and 1 cm.
2 Find the surface area of the rosette inside the equilateral triangle with side a.
http://img87.imageshack.us/img87/2590/graph2dj9.png

Homework Equations

The Attempt at a Solution

I have no idea what to do with the first one.For the 2nd one the area of the rosette inside the triangle should be the area of 3 segments minus the area of the triangle.
Here's a picture of what I did, with one circle only:
http://img339.imageshack.us/img339/4650/circlerd9.png
This is what I got: $$\frac{a^2}{6}(2 \pi - \frac{3 \sqrt {3} }{2})$$
But the book says it's $$\frac{a^2}{6}(2 \pi - 3 \sqrt {3} )$$, so can anyone check it?

 

[Gib Z]

Precalc? I have no idea on the 2nd one, the first one you have you do a few things.First develop an expression for the area of the quadrilateral using Herons Formula for triangles generalized, i can't rememeber the precise name.

$$A=\sqrt{(s-a)(s-b)(s-c)(s-d)}$$ where S = a+b+c+d, a b c and d are the lengths of the sides.

Then draw a line from A to B and A to C. Use the cosine rule to find an expression for the angles at 01 and 02. Using those angles, you can see how much of the circles area it encompasses. Now find the area of the sectors and subtract from the rectangle.

You won't get a very nice answer.

For then 2nd one, what is it that you want us to check? It isn't very clear.

 

[kristo]

Hey, thanks for your reply.
I had another go at the 1st problem and I solved it, got the same answer as the book. I did differently than you, though, using the congruence theorem and some trig.
http://xs.to/xs.php?h=xs114&d=07170&f=matenurk.png

Oh and there's a tiny difference between mine and the book's answer for the 2nd problem, just wanted to check who is right..
Thanks again!