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) $\frac{1}{2}$ar (ΔABC) (c) $\frac{1}{3}$ar (ΔABC) (d) $\frac{1}{4}$ar (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). MathematicsRD Sharma (2017)Standard IX

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