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Question

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

(a) 28 cm2

(b) 48 cm2

(c) 96 cm2

(d) 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.

Now ABCD is a parallelogram which means

……..(1)

……(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.

……(3)

Similarly ,

……(4)

Adding 3 and 4 we get,

Hence the correct answer is option (b).


Mathematics
RD Sharma (2017)
Standard IX

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