Question

4. Suppose P, Q and R are the mid-points
of sides of a triangle of area 128 cm?
If a triangle ABC is drawn by joining
the mid-points of sides of triangle
POR, then what is the area of triangle
ABC?
(a) 4 cm2
(b) 8 cm2
(c) 16 cm?
(d) 32 cm​

Answer 1

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9th

Maths

Quadrilaterals

Mid Point Theorem

In a triangle ABC , points...

MATHS

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:

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ANSWER

Between the triangle ARP and CRQ applying mid point theorem

RP ∥ BC and

RP =

2

1

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

Answer 2

Answer:

5 sqcm

Step-by-step explanation:

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