The area of the rhombus (in cm
2
) having each side equal to 13cm and one of its diagonals equal to 24cm is:

The diagonals of a rhombus bisect each other at right angles (90
∘
).
Let the diagonals be d
1
​
and d
2
​
.
Given:

Side (a) = 13cm

Diagonal d
1
​
=24cm⟹
2
d
1
​

​
=12cm

Using the right-triangle property of a rhombus side and half-diagonals:

(
2
d
1
​

​
)
2
+(
2
d
2
​

​
)
2
=a
2

12
2
+(
2
d
2
​

​
)
2
=13
2

144+(
2
d
2
​

​
)
2
=169
(
2
d
2
​

​
)
2
=169−144=25
2
d
2
​

​
=
25

​
=5cm⟹d
2
​
=10cm
Now, calculate the area of the rhombus:

Area=
2
1
​
×d
1
​
×d
2
​
=
2
1
​
×24×10=120cm
2