SOLUTION: The adjascent sides of a paralellogram ABCD measures 34cm and 20cm and diagnal AC measures 42cm. Find area of paralellogram with diagram.

Algebra ->  Parallelograms -> SOLUTION: The adjascent sides of a paralellogram ABCD measures 34cm and 20cm and diagnal AC measures 42cm. Find area of paralellogram with diagram.      Log On


   

Question 986276: The adjascent sides of a paralellogram ABCD measures 34cm and 20cm and diagnal AC measures 42cm. Find area of paralellogram with diagram.
Answer by ikleyn(52807) About Me  (Show Source):
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The area of the parallelogram is twice the area of the triangle with the side measures of  34 cm,  20 cm  and  42 cm.

Use the Heron's formula for the area of a triangle  (see the lesson  Proof of the Heron's formula for the area of a triangle  in this site).

The semi-perimeter of the triangle is  s = %2834%2B20%2B42%29%2F2 = 96%2F2 = 48 cm.

Then the area of the triangle is  A = sqrt%2848%2A%2848-42%29%2A%2848-20%29%2A%2848-34%29%29 = 336 cm%5E2.

Hence,  the area of the parallelogram is twice this value,  i.e. 672 cm%5E2.