AE || BC and D is the mid-point of BC. If area △ABC = 84 cm2, what is area of

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

Options:

A . 21

c m^{2}

B . 42

c m^{2}

C . 63

c m^{2}

D . 84

c m^{2}

Answer: Option B
:
B

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) ( $∵$ D is the mid point)
So, Area (△ABC) = 2 × Area (△BDE)
Area (△BDE) = 42 $c m^{2}$

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