In a triangle $△ A B C$ , points P, Q and R are the mid-points of the sides AB, BC and CA respectively. If the area of the triangle ABC is 20 sq.units, then area of the triangle PQR equal to:

10

sq. units

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5 \sqrt{3}

sq. units

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5

sq. units

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5.5

sq. units

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Solution

The correct option is C $5$ sq. units
Between the triangle ARP and CRQ applying mid point theorem
RP $∥$ BC and
RP $= \frac{1}{2}$ 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 $Δ A R P = A r e a Δ$ 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 $=$ $5 s q . c m$

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In a triangle △ABC, points P, Q and R are the mid-points of the sides AB, BC and CA respectively. If the area of the triangle ABC is 20 sq.units, then area of the triangle PQR equal to:

In a triangle $△ A B C$ , points P, Q and R are the mid-points of the sides AB, BC and CA respectively. If the area of the triangle ABC is 20 sq.units, then area of the triangle PQR equal to: