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Question -

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



Answer -

Given: In figure:
(1) ∠AOB = 90°
(2) AC = BC,
(3) OA = 012 cm,
(4) OC = 6.5 cm.
To find: Area of ΔAOB
Calculation:
It is given that AC = BC where C is the mid point of AB
We know that the mid point of hypotenuse of right triangle is equidistant from the vertices
Therefore
CA = BC = OC
⇒ CA = BC = 6.5
⇒ AB = 2 × 6.5 = 13 cm
 
Now in triangle OAB use Pythagoras Theorem
So area of triangle OAB
 
Hence area of triangle is 

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