Question

The perimeter of an equilateral triangle is 36cm. Calculate its area.

Answer 1

Answer:

Area of a equilateral triangle is $36\sqrt{3} (cm)^2$

Step-by-step explanation:

The perimeter of an equilateral triangle is 36 cm

we know that,

The perimeter of an equilateral triangle =3(side)

                        $3(side)=36 cm\\ \\ side=12 cm$

Area of a equilateral triangle=

                                          $\frac{\sqrt{3} }{4} (side)^2\\ \\ =\frac{\sqrt{3} }{4}(12)^2\\ \\ =\frac{\sqrt{3} }{4}(144)=36\sqrt{3}$

Answer 2

Answer:

∴  Area of an equilateral triangle is $62.35$ $cm^{2}$.  

Step-by-step explanation:

• In context to question asked,
• The perimeter of an equilateral triangle is $36$ cm.
• We have to find the area of the triangle.
• We know that, equilateral triangle has all the three sides equal in length.
• Let, $x$ be the length of side of equilateral triangle.
• Perimeter of triangle is the sum of all sides of a triangle.
• The formula for perimeter of equilateral triangle having side $x$ is given by,

        $x+x+x=36$

              ∴ $3x=36$

               ∴ $x=\frac{36}{3}$

               ∴ $x=12$ cm

• Now, the formula for area of equilateral triangle is given by,

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

                                          = $\frac{\sqrt{3} }{4} *12^{2}$

                                          = $\frac{\sqrt{3}}{4} *144$

                                          = $\sqrt{3} *36$

                                          = $62.35$ $cm^{2}$

• ∴  Area of an equilateral triangle is $62.35$ $cm^{2}$.