Question

AE || BC and D is the midpoint of BC. If area $△ABC$ = 84 square cm, what is the area of $△BDE$?

• A. 21 square cm
• B. 42 square cm
• C. 63 square cm
• D. 84 square cm

Answer 1

The correct option is B

42 square cm

If we draw EC, we can see that $△ABC$ and $△BEC$ will have equal area.
In $△ABC$ and $△BDC$ the altitude is the same but the length of the base is different.

Base length of ($△ABC$) = 2 × Base length of ($△BDE$)

So, Area ($△ABC$) = 2 × Area ($△BDE$)

Hence, Area ($△BDE$) = $\frac{84}{2}$ = 42 square cm