Question

if D,E,F are respectively the mid point of the side BC,CA and AB of triangle abc and the area of triangle abc is. 24 sq.cm then the area of triangle DEF is​

Answer 1

Answer:

area of ΔDEF =6cm²

Step-by-step explanation:

Given:

ΔABC, D,E and F are mid points of AB,BC,CA respectively.

In ΔABC

F is mid point of AC and D is mid point of AB.

Thus, by Mid point theorem, we get

FD= 1/2 of CB,

FD=CE and FD∥CE ...(1)

Similarly,

DE=FC and DE∥FC ...(2)

FE=DB and FE∥DB ...(3)

From (1), (2) and (3)

□ADEF, □DBEF, □DECF are parallelograms.

The diagonal of a parallelogram divides the parallelogram into two congruent triangles.

Hence, Δ DEF≅Δ ADF

Δ DEF≅Δ DBE

Δ DEF≅Δ FEC

Or, Δ DEF≅Δ ADF≅Δ ECF≅ΔADF

Thus, mid points divide the triangle into 4 equal parts.

Now,

A(Δ DEF)= 1/2 A(Δ ABC)

A(Δ DEF)= 1/4 *24

A(Δ DEF)=6 cm²