Ram and Sham are making two different Kite s in the shape of Rhombuses.

Perimeter = 4 * a = 40 cm

=> the side of the Rhombus = 10 cm.

The internal angles and the diagonal sizes, and hence the areas of the two kites are different.

*Ram's Kite*:

One of the diagonals of the kite is an integral multiple of 12 cm scale used.

The diagonals of the Kite of Ram are: X = 12 * k cm (a multiple of 12 cm, as a scale of 12 cm is used). The other diagonal is W cm, let us say.

Since in a Rhombus, 4 a² = X² + W²

4* 10² = 12² * k² + W^2

X, k are non zero positive integers and W is a positive real number.

if k = 1, then W = 16

So the diagonals are: 12 cm and 16 cm.

So the area of Ram's kite = 12 * 16/2= 96 cm²

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*Similarly for Sham's kite*:

one of the diagonals of the kite is an integral multiple of 16 cm scale.

4 * a² = (16 k)² + N²

here k, N are positive and k is a positive integer.

4 * 100 = 256 * k² + N²

k = 1 and hence, N = 12 cm

So the diagonals are : 16 cm and 12 cm..

The area of the kite is : 16 * 12 / 2 = 96 cm²

The areas of blue and red paper are equal to 96 cm²