In parallelogram ABCD, sides AB = 5 AC = 13 AD = 12. Find its area.

univerkov | June 17, 2021 | education

Since the opposite sides of the parallelogram are equal, then CD = AB = 5 cm.

The diagonal AC of the parallelogram divides it into two triangles, ABC and ADC in which the three sides are equal, and therefore the triangles are equal.

In triangle ACD, according to Heron’s theorem, we define its area.

The semi-perimeter of the ACD triangle is equal to: p = (AC + CD + AD) / 2 = (13 + 5 + 12) / 2 = 30/2 = 15 cm.

Then Sacd = √р * (р – СD) * (р – АD) * (р – АС) = √15 * (15 – 5) * (15 – 12) * (15 – 13) = √15 * 10 * 3 * 2 = √900 = 30 cm2.

Then Savsd = 2 * Sasd = 2 * 30 = 60 cm2.

Answer: The area of the parallelogram is 60 cm2.

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