The figure obtained by joining the mid-points of the adjacent sides of a rectangle of sides 8 cm and 6 cm is :
a. a rectangle of area 24 cm²
b. a square of area 25 cm²
c. a trapezium of area 24 cm²
d. a rhombus of area 24 cm²

Solution:

It is given that

Length of rectangle = 8 cm

Breadth of rectangle = 6 cm

Consider E, F, G and H as the mid-points of sides AB, BC, CD and AD

EFGH is a rhombus

Diagonals are EG and HF

So EF = BC = 8 cm

HF = AB = 6 cm

We know that

Area of rhombus = Product of diagonals/ 2

By further calculation

= (8 × 6)/2

= 4 × 6

= 24 cm²

Therefore, the figure obtained is a rhombus of area 24 cm².

✦ Try This: The figure obtained by joining the mid-points of the adjacent sides of a rectangle of sides 5 cm and 3 cm is :

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

NCERT Exemplar Class 9 Maths Exercise 9.1 Problem 3

The figure obtained by joining the mid-points of the adjacent sides of a rectangle of sides 8 cm and 6 cm is : a. a rectangle of area 24 cm², b. a square of area 25 cm², c. a trapezium of area 24 cm², d. a rhombus of area 24 cm²

Summary:

The figure obtained by joining the mid-points of the adjacent sides of a rectangle of sides 8 cm and 6 cm is a rhombus of area 24 cm²

☛ Related Questions:

• In Fig. 9.4, the area of parallelogram ABCD is : a. AB × BM, b. BC × BN, c. DC × DL, d. AD × DL
• In Fig. 9.5, if parallelogram ABCD and rectangle ABEF are of equal area, then : a. Perimeter of ABCD . . . .
• The mid-point of the sides of a triangle along with any of the vertices as the fourth point make a p . . . .