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In the below fig. ∠AOB = 90°, AC = BC, OA = 12 cm and OC = 6.5 cm. Find the area of

ΔAOB.

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#### Solution

Since, the midpoint of the hypotenuse of a right triangle is equidistant from the vertices

∴ CA = CB = OC

⇒ AB = 13 = 6.5cm

In a right angle triangle OAB, we have

AB^{2} = OB^{2} + OA^{2}

⇒ 13^{2} = OB^{2} + 12^{2}

⇒ OB^{2} = 13^{2 -} 12^{2} = 169 - 144 = 25

⇒ OB = 5

∵ ar (ΔAOB) = `1/2` (OA×OB) = `1/2` (12 ×5 ) = 30cm^{2}

Concept: Concept of Area

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