The mid-point of the sides of a triangle along with any of the vertices as the fourth point make a parallelogram of area equal to
a. 1/2 ar (ABC)
b. 1/3 ar (ABC)
c. 1/4 ar (ABC)
d. ar (ABC)

Solution:

If D, E and F are the mid-points of BC, AC and AB of triangle ABC, then all four triangles have equal area

ar (∆ AFE) = ar (∆ BFD) = ar (∆ EDC) = ar (∆ DEF) …. (1)

We know that

Area of ∆ DEF = 1/4 Area of ∆ ABC …. (2)

If D is considered as the fourth vertex

Area of parallelogram AFDE = Area of ∆ AFE + Area of ∆ DEF

From the equation (1)

Area of parallelogram AFDE = Area of ∆ DEF + Area of ∆ DEF

Area of parallelogram AFDE = 2 × Area of ∆ DEF

From equation (2)

Area of parallelogram AFDE = 2 × 1/4 Area of ∆ ABC

= 1/2 Area of ∆ ABC

Therefore, the area of the parallelogram is 1/2 ar (ABC).

✦ Try This: The figure obtained by joining the mid-points of the adjacent sides of a rectangle of sides 10 cm and 8 cm is :

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 9

NCERT Exemplar Class 9 Maths Exercise 9.1 Problem 6

The mid-point of the sides of a triangle along with any of the vertices as the fourth point make a parallelogram of area equal to a. 1/2 ar (ABC), b. 1/3 ar (ABC), c. 1/4 ar (ABC), d. ar (ABC)

Summary:

The mid-point of the sides of a triangle along with any of the vertices as the fourth point make a parallelogram of area equal to 1/2 ar (ABC)

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