Question

In the figure,D and E are the mid point of the sides AC and BC respectively of ∆ABC .if ar(∆BED)=12cm^2,then at(∆AEC)=​

Answer 1

Step-by-step explanation:

In ∆ DBC , point E is the mid point of BC , thus DE is a median of this ∆. we know

that median of a triangle divides the ∆ in two triangles having equal areas.

Therefore area of ∆ CED = area of ∆ BED. …………………..(1),

putting area of ∆ BED= 12cm^2. in eqn.(1)

Area of ∆ CED = 12 cm^2.

Thus ,area of ∆ BDC= area of ∆ BED+area of ∆ CED = 12+12 = 24 cm^2………..(2).

In ∆ BAC , BD is a median , therefore

Area of ∆BDA = area of ∆ BDC. , putting area of ∆ BDC=24cm^2 from eqn.(2).

Area of ∆ BDA = 24 cm^2.

Area of figure ABED = area of ∆ BDA + area of ∆ BED =24+12 =36 cm^2