In figure, ∠AOB = 90°, AC = BC, OA = 12 cm and OC = 6.5 cm. Find th

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

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

Answer»

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