Question

Find the area of ΔAOB 3√3 un2 4.5√3 un2 9√3 un2

Answer 1

Answer:

The area of the ΔAOB is $9\sqrt{3}\ unit^{2}$ .

Step-by-step explanation:

As given the figure

OA = OB = 6 unit

(Radius of the circle.)

In ΔAOB

As the two sides of a triangle thus there opposite angles are also equal .

∠A = ∠B

Let us assume that ∠A = ∠B = x°

∠A + ∠O + ∠B = 180°

(By using the angle sum property of a triangle.)

∠O = 60°

x° + 60° + x° = 180°

2x = 180 - 60

2x = 120

$x = \frac{120}{2}$

x = 60

∠A = ∠B = 60°

Thus

∠A = ∠B = ∠O = 60°

As all the angles of the ΔAOB are 60° thus ΔAOB is a equilateral triangle .

Also all the sides of the ΔAOB are also equal i.e AB = OA = OB = 6 unit .

Formula

$Area\ of \ a\ equilateral\ triangle = \frac{\sqrt{3}}{4} a^{2}$

Where a is the side of the equilateral triangle .

a = 6 unit

Put in the above formula

$Area\ of \ a\ equilateral\ triangle = \frac{\sqrt{3}}{4}\times 6^{2}$

6² = 36

$Area\ of \ a\ equilateral\ triangle = \frac{\sqrt{3}}{4}\times 36$

$Area\ of \ a\ equilateral\ triangle = 9\sqrt{3}\ unit^{2}$

Therefore the area of the ΔAOB is $9\sqrt{3}\ unit^{2}$ .