Question

In a triangle ABC points P,Q,R are the mid points of sides ab, bc, ca respectively. if the area of triangle ABC is 20 sq.units then the area of the triangle PQR equal to

Answer 1

P, Q and R are the mid-points of the sides of triangle ABC

This means triangle ABC is 4 times the triangle PQR (mid point theorem)

This area of triangle ABC = 4 * area triangle PQR

20/4 = area triangle PQR

Area triangle PQR = 5cm^2

Answer 2

Between the triangle ARP and CRQ applying mid point theorem...

RP ∥ BC,

RP =½ , BC = CQ.

• And AR = RC ( R is the mid point of AC )

• again PR ∥ BC and AC is the transversal.

Therefore angle ARP = angle RCQ.

Therefore the triangles are congruent by SAS test.

Area ΔARP=AreaΔ RCQ.

⬜By applying the same midpoint theorem we can prove that each of the four triangles have the same area.⬜

• So, they divide the triangle into four equal areas.

Now total area = 20 sq. cm.

✍️Therefore area of the Δ PQR is 20 sq.cm divided by 4 = 5 sq.cm