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