Question

Let ABC be a triangle of area 24units² and PQR be a triangle formed by the midpoints of sides of ∆ABC. Then, the area of ∆PQR is :
a) 12 sq. Units
b) 6 sq. units
c) 4sq units
d) 3 sq units

Method needed

Answer 1

hello friend

your answer is in the given statement I hope you will be satisfied with my answer

thank you

please mark my answer as brain list

✌️✌️✌️✌️✌️✌️✌️✌️✌️✌️✌️✌️✌️✌️

Answer 2

Hey!!!

Good Afternoon

____________

We will use the theorem

=> The area of triangle formed by the mid points of the triangle is one fourth of the area of the original triangle.

For figure, refer to the attachment

Thus ar(∆PQR) = (1/4) ar(∆ABC)

Thus

=> ar(∆PQR) ⤵️


$= \frac{1}{4} \times 24$

= 6 cm² or 6 unit²

=> Derivation of the Theorem

Since P and Q are the mid points of AB and AC, PQ II BC ( By mid point Theorem of class 9)

And similarly QR II AB and PR II AC

Hence Now we have 3 parellogram in ∆ABC.

Also by Mid Point Theorem

=> 2PQ = BC
=> 2QR = AB
=> 2PR = AC

Thus we will prove that ∆ABC is similar to ∆PQR

and hence Proved

_______________

For doubts plz comment below

Or

Inbox me

______

Hope this helps ✌️