Answer question 3 and 4 please?

3. Let a = the unshaded region between Crescent A and the right triangle. Let b = the unshaded region between Crescent B and the right triangle.

The area of Semicircle C = C + a + b

The area of Semicircle A = A + a

The area of Semicircle B = B + b

From the Pythagorean theorem we know that the sum of the areas of Semicircles A and B should be equal to the area of semicircle C; in other words:

A + a + B + b = C + a + b

Subtracting a and b from both sides gives:

A + B = C

Q.E.D.

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4. The area of the annulus = area of big circle - area of little circle

Let R = the radius of the big circle. Let r = the radius of the little circle.

The radius of the big circle is the hypotenuse of a right triangle whose legs are half of L and the radius of the little circle; in other words:

R² = (1/2 L)² + r²

R = √(L²/4 + r²)

So the area of the big circle is:

A = πR²

A = π(√(L²/4 + r²))²

A = π(L²/4 + r²)

A = πL²/4 + πr²

The area of the little circle is:

a = πr²

So the area of the annulus, A - a, is:

A - a = (πL²/4 + πr²) - πr²

A - a = πL²/4

Q.E.D.

I hope that helps. Good luck!