Question

AAOB is right triangle with ZAOB = 90°. C is mid-point of AB, OA = 12 cm and
OC = 6.5 cm, then ar (AOB) = :
A)20 cm2
{B) 30 cm2
(C) 40 cm2
(D) 45 cm2​

Answer 1

AnswEr :

• ar(AOB) = 30 cm² [Option B]

Given :

• ∠AOB = 90°

• AB = BC

• OA = 12 cm

• OC = 6.5 cm

To Find :

• Area of ∆ABC = ?

Solution :

In ∆AOB,

CA = CB = OC [midpoint of the hypotenuse of right angled triangle is equidistant from its vertices!! ]

Hence ,

➝ AB = CA + CB

➝ AB = 6.5 + 6.5

➝ AB = 13 cm

By Pythagoras theorem,

➝ AB² = OB² + OA²

➝ 13² = OB² + 12²

➝ OB² = 13² - 12²

➝ OB² = 169 - 144

➝ OB² = 25

➝ OB = 5 cm

Now,

➝ Area of ∆AOB = 1/2 × (OA × OB)

➝ Area of ∆AOB = 1/2 × (12 × 5)

➝ Area of ∆AOB = 1/2 × (60)

➝ Area of ∆AOB = 30 cm²

⠀⠀━━━━━━━━━━━━

$\dag \large \ { \underline{ \underline{ \sf{ \red{Additional \ Information :}}}}}$

• Mid point theorem :

Any line segment in a triangle joining the midpoint of 2 sides of the triangle is said to be parallel to its 3rd side and is also half of the length of the 3rd side !!

• Pythagoras theorem :

In any right angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides !!

• Hypotenuse² = Perpendicular² + Base²

• H² = P² + B²

⠀⠀━━━━━━━━━━━━