Find the area of a rhombus one side of which measures \(10\) cm and one diagonal \(12\) cm. একটি সমবাহু চতুর্ভুজের একটি বাহু \(10\) সেমি এবং একটি কর্ণ \(12\) সেমি হলে, ক্ষেত্রফল কত?

In a rhombus, diagonals bisect each other at right angles.

Side \(= 10\)

One diagonal \(= 12\)

Half diagonal:

\[ \frac{12}{2} = 6 \]

Let the other half diagonal \(= x\)

Using Pythagoras:

\[ 10^2 = 6^2 + x^2 \] \[ 100 = 36 + x^2 \] \[ x^2 = 64 \] \[ x = 8 \]

Other diagonal:

\[ 2x = 16 \]

Area of rhombus:

\[ \text{Area} = \frac{1}{2} \times 12 \times 16 \] \[ = 96 \]

Therefore, Area = \[ 96 \text{ cm}^2 \]