# The Area of the Figure Formed by Joining the Mid-points of the Adjacent Sides of a Rhombus with Diagonals 16 Cm and 12 Cm is - Mathematics

MCQ

The area of the figure formed by joining the mid-points of the adjacent sides of a rhombus with diagonals 16 cm and 12 cm is

•  28 cm2

•  48 cm2

• 96 cm2

• 24 cm2

#### Solution

Given: Rhombus with diagonals measuring 16cm and 12 cm.

To find: Area of the figure formed by lines joining the midpoints of the adjacent sides.

Calculation: We know that, ‘Area of a rhombus is half the product of their diagonals’.

H and F are the midpoints of AD and BC respectively.

AH = 1/2 AD

BE = 1/2 BC

Now ABCD is a parallelogram which means

AD = BC

1/2AD = 1/2BC

AH = BF      ……..(1)

AH || BF  ……(2)

From 1 and 2 we get that ABFH is a parallelogram.

Since Parallelogram FHAB and ΔFHE are on the base FH and between the same parallels HF and AB.

∴ ar (Δ FHE ) = 1/2 ar ( "||"^(gm) FHAB )    ……(3)

Similarly ,

ar (ΔFHG) = 1/2ar ("||"^(gm) FHDC) ……(4)

Adding 3 and 4 we get,

ar (Δ FHE ) + ar (ΔFHG) = 1/2 ar ("||"^(gm) FHAB)+1/2ar("||"^(gm)FHDC)

ar (EFGH) = 1/2 (ar("||"^(gm) FHAB ) + ar ("||"^(gm) FHDC))

ar (EFGH) = 1/2 (ar("||"^(gm) ABCD))

ar (EFGH) = 1/2 (1/2 (16xx12))

ar (EFGH) = 1/4 (16 xx 12)

ar (EFGH) = 48  cm^2

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 14 Areas of Parallelograms and Triangles
Q 7 | Page 61