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In the Below Fig. ∠Aob = 90°, Ac = Bc, Oa = 12 Cm and Oc = 6.5 Cm. Find the Area of δAob. - Mathematics

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

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Solution

Since, the midpoint of the hypotenuse of a right triangle is equidistant from the vertices

∴ CA = CB = OC

⇒ AB = 13 = 6.5cm 

In a right angle triangle OAB, we have

AB2 = OB2 + OA2 

⇒ 132 = OB2 + 122

⇒ OB2 = 132 - 122 = 169 - 144 = 25

⇒ OB = 5 

∵ ar (ΔAOB) = `1/2` (OA×OB) = `1/2` (12 ×5 ) = 30cm2

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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 14 Areas of Parallelograms and Triangles
Exercise 14.3 | Q 4 | Page 44
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