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Question

The mid-points of the sides of a triangle ABC along with any of the vertices as the fourth point make a parallelogram of area equal to

(a) ar (ΔABC)

(b) 12ar (ΔABC)

(c) 13ar (ΔABC)

(d) 14ar (ΔABC)


Solution

Given: (1) ABCD is a triangle.

(2) mid points of the sides of ΔABC with any of the vertices forms a parallelogram.

To find: Area of the parallelogram

Calculation: We know that: Area of a parallelogram = base × height

Hence area of ||gm DECF = EC × EG

area of ||gm DECF = EC × EG

area of ||gm DECF = (E is the midpoint of BC)

area of ||gm DECF =

area of ||gm DECF =

Hence the result is option (b).


Mathematics
RD Sharma (2017)
Standard IX

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