Question

An equilateral triangle has an apothem measuring 2.16 cm and a perimeter of 22.45 cm. What is the area of the triangle, rounded to the nearest tenth?

Answer 1

First of all, both apothem and perimeter are given which are not essential,
meaning to say...as it is an equilateral triangle any one of the quantity is sufficient to find the length of the side and thus the area

Apothem for equilateral triangle =(√3)/6  × l

Perimeter for equilateral triangle =3l

Both will give the same length of sides....but we will use perimeter data to make our calculations simpler

So,
3l=22.45
l=7.483 cm

Area of equilateral triangle = (√3/4) × l²
                                            =(√3/4) × (7.483)²
                                            =24.25  cm²

So, 
The area of triangle is 24.25 cm²