What is the type of the figure obtained by joining the midpoints of adjacent sides of a rectangle of sides 8 cm and 6 cm?

Text Solution

a rectangle of area `24 cm^(2)`a square of area `25 cm^(2)`a trapezium of area `24 cm^(2)`a rhombus of area `24 cm^(2)`

Answer : D

Solution : We know that , on joining the mid-points of the adjacent sides of a rectangle, we get a rhombus. <br> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/ARH_NCERT_EXE_MATH_IX_C09_S01_003_S01.png" width="80%"> <br> Here, length of rectangle ABCD = 8 cm <br> and breadth of rectangle ABCD = 6 cm <br> Let E, F, G and H are the mid-points of the sides of rectangle ABCD, then EFGH is a rhombus. <br> Then, diagonal of rhombus EFGH are EG and HF. <br> Here, EG = BC = 8 cm <br> and HF = AB = 6 cm <br> `therefore` Area of rhombus `= ("Product of diagonals")/(2)` <br> `= (8xx6)/(2) = 4 xx 6 = 24 cm^(2)` <br> Hence, joining the mid-points of the adjacent sides of a rectangle forms a rhombus of area `24 cm^(2)`.

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.

Explanation:

Given: Rectangle with sides 8 cm and 6 cm

To find: Area of the figure which is formed by joining the midpoints of the adjacent sides of rectangle.

Calculation: Since we know that area of rhombus = `1/2 (d_1 xx d_2)`

For rhombus EFGH, EG is the one diagonal which is equal to DA

FH is the other diagonal which is equal to AB

Area of rhombus = `1/2 (d_1 xx d_2)`

Area of rhombus = `1/2 ( 8 xx 6)`

Area of rhombus = `1/2 (48)`

Area of rhombus = 24 cm2