# 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)

**☛ Related Questions:**

- Two parallelograms are on equal bases and between the same parallels. The ratio of their areas is a. . . . .
- ABCD is a quadrilateral whose diagonal AC divides it into two parts, equal in area, then ABCD a. is . . . .
- If a triangle and a parallelogram are on the same base and between same parallels, then the ratio of . . . .

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