Triangle Area

As shown in the figure, ABCD is a rectangle. AD = 6, CD = EF = 3, and CG = 2. Find the shaded area.

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In square ABCD, AB = 1. BD and AC are arcs of radius 1. Two shaded areas

are the same. Find the difference of the unshaded areas.

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If ABCD is a 2 × 2 square, E is the midpoint of AB , F is the

midpoint of BC , AF and DE intersect at I, and BD and AF intersect at H, then the area of quadrilateral BEIH is

In triangle ABC, C is a right angle and M is on AC. A circle with radius r is centered at M, is tangent to AB, and is tangent to BC at C. If AC = 5 and BC = 12, compute r.

A wire of length of a is used to form an equilateral triangle with the area of b. Let P be any point inside the equilateral triangle. Find the sum of the distances from P to each side.