Question

AE || BC and D is the mid-point of BC. If area $△ABC$ = 84 $c{m}^2$, what is area of $△BDE$?

• A. 21$c{m}^2$
• B. 42$c{m}^2$
• C. 63 $c{m}^2$
• D. 84 $c{m}^2$

Answer 1

The correct option is B 42$c{m}^2$

If we draw EC, we can see that △ABC and △BEC will have equal area. Because triangles on same base and between same parallels are equal in area. In △ABC and △BDE the altitude is same but the length of the base is different. Base length (△ABC) = 2 × Base length (△BDE) ($\because$ D is the mid point) So, Area (△ABC) = 2 × Area (△BDE) Area (△BDE) = 42 $c{m}^2$