In the figure abc and xby are isosceles triangles. ac=6 cm. and xy=4 cm. find the area of the shaded region.

Area of the triangle is expressed by the product of the base and the height divided by two. This is from the idea that a parallelogram having an area of length times width can be divided yielding to two triangles. 

Area of shaded region = Area of triangle ABC - Area of triangle XBY
Area of triangle ABC = (6) (6) / 2 = 18 cm^2
Area of triangle XBY = (4) (4) / 2 = 8 cm^2
Area of shaded region = 18 - 8 = 10 cm^2