Question

What is this trying to ask me ???

Answer 1

Given :

In ∆ABC,

• ∠A = 60°
• ∠B = 60°
• BC = 12 units
• ∠BDC = 90°

To Find :

• Area of ∆ABC = ?

Solution :

As, we have :

• ∠A = 60°
• ∠B = 60°

So, By angle sum property of triangle :

∠A + ∠B + ∠C = 180°

`\tt : \implies 60\degree + 60\degree + \angle C = 180\degree`

`\tt : \implies 120\degree + \angle C = 180\degree`

`\tt : \implies \angle C = 180\degree - 120\degree`

`\tt : \implies \angle C = 60\degree`

Now, we have :

• ∠A = 60°
• ∠B = 60°
• ∠C = 60°

As, all angles are of same length, therefore it is a equilateral triangle.

We know that sides of equilateral triangle are equal.

`\tt : \implies AB = BC = AC`

Now, we have BC = 12 units.

Hence, all sides are of 12 units.

Now, we know that area of equilateral triangle is :

`\large \underline{\boxed{\bf{Area_((equilateral \: triangle)) = (√(3))/(4) side^(2)}}}`

`\tt : \implies Area = (√(3))/(4) * (12 \: units)^(2)`

`\tt : \implies Area = \frac{√(3)}{\cancel{4}} * \cancel{144} \: units^(2)`

`\tt : \implies Area = √(3) * 36 \: units^(2)`

`\tt : \implies Area = 36√(3) units^(2)`

So, Area of given triangle is 36√3 units².