Question

Find the area of an equilateral triangle whose perimeter is 18cm. Also find the hight. give me this answer fastly I really need this​

Answer 1

Step-by-step explanation:

perimeter of equilateral triangle = 3a

• 18cm = 3a
• a = 6cm

the area of an equilateral triangle =

• $\frac{ \sqrt{3} }{4} {a}^{2}$
• $\frac{ \sqrt{3} }{4} \times {6}^{2}$
• $\frac{ \sqrt{3} }{4} \times 36$
• $area \: = 9 \sqrt{3} cm^2$

height of equilateral triangle=

• $\frac{ \sqrt{3} }{2} \times a$
• $\frac{ \sqrt{3} }{2} \times 6$
• $height = 3 \sqrt{3} cm$

Answer 2

Answer:

$\large\boxed{\sf{area = 9 \sqrt{3} }}$

$\large\boxed{\sf{height = 3 \sqrt{3} }}$

Step-by-step explanation:

According to the information given in the question is

Perimeter=18cm

We need to find the area and height of the equilateral triangle.

Before we start let's learn what is equilateral triangle.

A equilateral triangle is a type of triangle in which all the sides and angles are .

Before finding area we have to find it's side

Perimeter=3×side

$\large\boxed{\sf{18cm= 3 \times side}}$

$\large\boxed{\sf{ \implies \frac{18cm}{3} = side}}$

$\large\boxed{\bf{6cm = side}}$

Area of equilateral triangle

$\large\boxed{\sf{ \implies \frac{ \sqrt{3} }{4} {s}^{2} }}$

On substituting values we get,

$\large\boxed{\sf{ \frac{ \sqrt{3} }{4} \times {(6cm)}^{2} }}$

$\large\boxed{\sf{ \frac{ \sqrt{3} }{4} \times 36cm^{2} }}$

$\large\boxed{\sf{ \sqrt{3} \times {9cm}^{2} }}$

$\large\underline{\bf{9 \sqrt{3} {cm}^{2} }}$

Now, height of equilateral triangle

$\large\boxed{\sf{ \frac{ \sqrt{3} }{2} s}}$

$\large \boxed{\sf{ \frac{ \sqrt{3} }{2} \times 6cm }}$

$\large\boxed{\sf{ \sqrt{3} \times 3cm }}$

$\large\boxed{\bf{3 \sqrt{3}cm }}$