A square and an equilateral triangle have a side in common. If side of triangle is cm long, find the perimeter of figure formed (Fig. 2.8).

Given:

Square BCDE and an equilateral triangle ABC have a common side BC

Side of triangle is cm

Formula UsedTheory:

All sides of square are equal

All sides of equilateral triangle are equal

If side of triangle is cm

Then;

AB = BC = CA = cm

∴ In square BCDE

If BC = cm ∵ BC is common in both triangle and square

As all sides of square are equal

BC = CD = DE = EB = cm

∴ All sides of equilateral triangle and square are equal

By joining triangle and square as in figure above

It forms a pentagon ABDEC

With sides AB = BD = DE = EC = CA = cm

⇒ Perimeter of ABDEC = AB + BD + DE + EC + CA

=

= 5 × cm

= cm

Conclusion: Perimeter of above figure is cm