Triangle Area

The area of triangle ABC is $$16\ \ cm^2$$ . D and E are midpoints of AB and AC, respectively. F is a point on BC such that BF = 3 cm. Find the
area of triangle DEF.

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

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.

AM is the median of $$\Delta ABC$$ . D is any point on MC such that ME//AD. Find the ratio between the area of the $$\Delta BDE$$ and the area of the quadrilateral $$AEDC$$ .

As shown in the figure, BF and AC cut the rectangle ABCD into 4 regions. The area of $$\Delta ECF$$ is $$4\ \ cm^2$$ and the area of $$\Delta CEB$$ is $$6\ cm^2$$ . Find
the area of quadrilateral $$AEFD$$ .

As shown in the figure, $$\Delta ABC$$ is an obtuse triangle. M is the midpoint of BC. $$AE\perp AC$$ . MD//AE. What is the area of $$\Delta CDE$$ if the area of
$$\Delta ABC$$ is 2014?

In triangle ABC, $$\angle CBA\ =\ 72^0$$ , E is the midpoint of side AC, and D is a point on side BC such that $$2BC=CD$$ ; AD and BE intersect at F. The ratio of the area of ∆BDF to the area of
quadrilateral FDCE is

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.