In Fig. 15.77, ∠ AOB=90°, AC=BC, OA=12 cm and OC=6,5 cm. Find the area of Δ AOB.

Question

In Fig. 15.77, &#x2220; AOB=90&#xB0;, AC=BC, OA=12 cm and OC=6,5 cm. Find the area of &#x394; AOB.

Philoid · Accepted Answer

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 (OAB)

We have,

AB² = OB² - OA²

13² = OB² + 12²

OB = 5 cm

Therefore,

Area (Δ AOB) = (OA * OB)

= (12 * 5)

= 30 cm²