CPM Homework Help : CCG Problem 6-56

Triangle, A B C, side, A C, horizontal & marked with 2 arrows, dashed horizontal line through vertex, B, also marked with 2 arrows, Dashed segment from vertex, A, perpendicular to horizontal line, labeled 3.6, dashed segment from vertex A to point labeled, E, on side, B C, segment labeled 3, segment, B E, labeled 2, segment, E C, labeled 4. Penelope measured several sides and heights of $ΔABC$ , as shown in the diagram at right. Find the area of $ΔABC$ twice, using two different methods.

Hint 1:

$A=\frac{1}{2}bh$

Remember: a base and a height must be perpendicular!
Which side can be used as a base? As the height?

Answer:

One method could be to use $\overline{BC}$ as the base and $\overline{AE}$ as the height.

$\text{Area = }{\frac{1}{2}}(6)(3)=9$

Hint 2:

Use another side as a base. But why is using $\overline{AB}$ as the base a bad idea?

Use $\overline{AC}$ as the base.