Look at the figure below. If the area of is, AD = DB, CE = 2 BE, then what is the area of?

cm^{2}

The key to this problem is to find the relation between the area of and the area of. We draw line segment CD to create triangles with same heights. Since andshare a same height, but CE is 2 times BE, thus has an area two times that of . Since and share a same height, and AD = DB, thus the areas of these two triangles are the same. If we call the area of , (1) , then is 2 (1) , and

= (1) + 2 (1) = 3 (1) .

Thus

= (1) + 2 (1) + 3 (1) = 6 (1) .

We already know this equals 24. So we have

6 (1) = 24, thus (1) = 24 cm^{2} ÷ 6 = 4 cm^{2}