The area of a parallelogram ABCD in which AB = 28 cm, BC = 26 cm and diagonal AC = 30 cm is ____ $c m 2$ .

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Detailed Solution

The area of a parallelogram ABCD in which AB = 28 cm, BC = 26 cm and diagonal AC = 30 cm is 672

c m 2

Given a parallelogram ABCD in which AB = 28 cm, BC = 26 cm and diagonal AC = 30 cm.
The value of semi perimeter (s) for triangle ABC is,

s = a + b + c 2

⇒ s = 26 + 30 + 28 2

⇒ s = 42 c m

Now using Heron’s formula in triangle ABC,

A = s s − a s − b s − c

⇒ A = 42 42 − 26 42 − 30 42 − 28 ⇒ A = 42161214 ⇒ A = 14 × 14 × 3 × 3 × 16 × 4

⇒ A = 14 × 3 × 4 × 2

⇒ A = 336 c m 2

Now, as the diagonal divides the parallelogram into 2 triangles of equal areas.
Area of parallelogram is,

⇒ A r e a o f p a r a l l e l o g r a m = 2 × 336 c m 2

⇒ A r e a o f p a r a l l e l o g r a m = 672 c m 2

Hence, area of parallelogram is

672 c m 2 .

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