### The two adjacent sides of a parallelogram are 3 cm and 4 cm. If one of its diagonals is 5 cm, find the area of the parallelogram.

12 cm2

Step by Step Explanation:
1. Take a look at the representative image below:

We can see that ABC is a triangle.
Also we know the length of all the sides. We can therefore use Heron's formula:
S =
 a + b + c 2
[Where a, b and c are the sides.]
=
 3+4+5 2

= 6
2. Area of the triangle ABC = $\sqrt{ S(S-a)(S-b)(S-c) }$
= $\sqrt{ 6(6-3)(6-4)(6-5) }$
= 6 cm2
3. Now, the area of the parallelogram = 2 × Area of the triangle ABC
= 2 × 6
= 12 cm2