Question

In triangle ABC, D and E are points on side BC such that CD=DE=EB. If ar(ABC)=27 cm^3.find ar(ADE).​

Answer 1

Step-by-step explanation:

the question is wrong. how can an area be cubic centimetre

Answer 2

The area of triangle(ADE) $=9cm^2$

Step-by-step explanation:

Fiven by question,

△AEC, CD = DE, AD is a median.

∴ ar(△ACD) = ar(△ADE)     ......(i)

To find, ar(△ADE) = ?

We know that,

The median divides a triangle into two triangles of equal areas,

In △ABD , DE = EB, AE is a median      

∴ ar(△ADE) = ar(△AEB) ---(ii)  

Using equation (i) and (ii), we get

ar(△ACD) = ar(△ADE) = ar(△AEB)

= $\dfrac{1}{3}$ ar(△ABC)

∴ ar(△ADE) = $\dfrac{1}{3}$ × 27

$=9cm^2$

Hence, the area of triangle(ADE) $=9cm^2$