Question

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

Answer 1

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

AB² = OB² + OA² 

⇒ 13² = OB² + 12²

⇒ OB² = 13^{2 -} 12² = 169 - 144 = 25

⇒ OB = 5 

∵ ar (ΔAOB) = `1/2` (OA×OB) = `1/2` (12 ×5 ) = 30cm²