Question

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

Find the area of Δ AOB.

Answer 1

Since, 

The mid-point of the hypotenuse of a right triangle is equidistant from the vertices 

Therefore, 

CA = CB = OC 

CA = CB = 6.5 cm 

AB = 13 cm 

In right (ΔOAB) 

We have,

 AB² = OB² - OA² 

13² = OB² + 12² 

OB = 5 cm 

Therefore, 

Area (Δ AOB) = \(\frac{1}{2}\)(OA x OB) 

=\(\frac{1}{2}\)(12 x 5) 

= 30 cm²