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in Parallelograms by (56.3k points)

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

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Given: A triangle AOB, with ∠AOB = 90o, AC = BC, OA = 12 cm and OC = 6.5 cm 

As we know, the midpoint of the hypotenuse of a right triangle is equidistant from the vertices. 

So, CB = CA = OC = 6.5 cm 

AB = 2 CB = 2 x 6.5 cm = 13 cm 

In right ΔOAB: 

Using Pythagorean Theorem, we get 

AB2 = OB2 + OA2 

132 = OB2 + 122 

OB2 = 169 – 144 = 25 

or OB = 5 cm 

Now, Area of ΔAOB = 1/2(Base x height) cm2 

= 1/2(12 x 5) cm2 

= 30 cm2

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