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.
Answer:
12 cm2
- 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 =
[Where a, b and c are the sides.]a + b + c 2
=3+4+5 2
= 6 - Area of the triangle ABC = √S(S−a)(S−b)(S−c)
= √6(6−3)(6−4)(6−5)
= 6 cm2 - Now, the area of the parallelogram = 2 × Area of the triangle ABC
= 2 × 6
= 12 cm2