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.


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Answer:

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

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