Question

given P,Q,R are the midpoints of AB, BC, CA of triangle ABC. if thr area of triangle ABC is 20 sq.units then the area of triangle PQR in sq.units is

Answer 1

In triangle ABC, D, E and F are the midpoints of BC, CA and AB, respectively. If the area of ABC is 20 sq cm, what is the area of DEF?

When the midpoints of the three sides of any triangles are joined, we get 4 congruent triangles - ADE, DEF, DBF, EFC -each having an area one-fourth of the parent triangle. Hence area of DEF = 5 sq cm.

Answer 2

Answer:

The area of triangle PQR is 5 sq. units.

Step-by-step explanation:

Given a triangle ABC.

P,Q,R are the midpoints of AB, BC, CA

Area of triangle ABC is 20 sq.units

According to the midpoint theorem, 'the line segments joining the mid  points of the sides of a triangle divide the triangle into four congruent triangles'.

Therefore, the area of the $\triangle ABC$ is divided into 4 equal triangles of equal area.

And, the area of each triangle $=\frac{20}{4} =5sq. units$

Hence, the area of triangle PQR is 5 sq. units.