102k views
4 votes
What is this trying to ask me ???

What is this trying to ask me ???-example-1

1 Answer

4 votes

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.

User Frank R
by
7.0k points