Question

If one side of an equilateral triangle is 8 cm, find its area, height and perimeter.​

Answer 1

Answer:

Given :

• ✿ Side of an equilateral triangle = 8 cm

$\begin{gathered}\end{gathered}$

To Find :

• ✿ Area of Equilateral Triangle

$\begin{gathered}\end{gathered}$

Using Formula :

$\underline{\boxed{\sf{\pink{Area \:of \:an\:equilateral\:triangle=\frac{\sqrt{3}}{4}\: (side)^{2}}}}}$

$\underline{\boxed{\sf{\pink{Area \: of \: an \: triangle = \dfrac{ 1}{2} \times base \times height }}}}$

$\underline{\boxed{\sf{\pink{Perimeter \: of \: an \: triangle = 3a }}}}$

$\begin{gathered}\end{gathered}$

Solution :

Here

• All sides of triangle will be 8 cm because it is a equilateral triangle.

$\begin{gathered}\end{gathered}$

Finding area of equilateral triangle

$\begin{gathered} \qquad: \sf\implies \frac{\sqrt{3}}{4}\times 8^{2} \\ \\ \quad : \implies \sf\frac{\sqrt{3}}{4}\times 8\times 8 \\ \\ \qquad\sf: \implies 16\sqrt{3}\: cm^{2} \\ \\ \end{gathered}$

$\bigstar{\underline{\boxed{\pmb{\sf{ Area\:of \: equilateral\: \triangle=16\sqrt{3}\: cm^{2}}}}}}$

Hence, The area of equilateral triangle is 16√3 cm².

$\begin{gathered}\end{gathered}$

Now, Finding the height of equilateral triangle.

$\begin{gathered} : \implies\sf{Area \: of \: Triangle = \dfrac{ 1}{2} \times base \times height } \\ \\ : \implies \sf{16\sqrt{3} = \dfrac{1}{2} \times 8 \times height} \\ \\ : \implies \sf Height = \dfrac{(16\sqrt{3} \times 2)}{8}\\ \\ : \implies \sf Height = \frac{32\sqrt{3} }{8} \\ \\ : \implies \sf Height = \frac{ \cancel{32}\sqrt{3} }{\cancel{8}} \\ \\ : \implies\sf Height = 4\sqrt{3} \end{gathered}$

$\bigstar{\underline{\boxed{\pmb{\sf{ Height of Triangle = 4\sqrt{3} }}}}}$

Hence, The height of equilateral triangle is 4√3 cm.

$\begin{gathered}\end{gathered}$

Now, Finding the perimeter of equilateral triangle.

$\begin{gathered} \qquad : \implies\sf Perimeter \: of \: \triangle = 3a \\ \\ : \implies\sf Perimeter \: of \: \triangle = 3 \times 8 \\ \\ \qquad : \implies\sf Perimeter \: of \: \triangle = 24 \: cm\end{gathered}$

$\bigstar{\underline{\boxed{\pmb{\sf{Perimeter \: of \: Triangle = 24 \: cm }}}}}$

Hence, The perimeter of equilateral triangle is 24 cm.

$\begin{gathered}\end{gathered}$

Answer :

• ✱ The area of equilateral triangle is 16√3 cm².
• ✱ The height of equilateral triangle is 4√3 cm.
• ✱The perimeter of equilateral triangle is 24 cm.

––––––––––––––––––––––

Answer 2

Answer:

Area is 16√3 cm², Perimeter is 24 cm and height is 4√3.

Step-by-step explanation:

Given :

• One side of equilateral triangle is 8 cm.

To find :

• Area, height and perimeter of triangle.

Solution :

All sides of triangle are 8 cm because sides of equilateral triangle are equal.

We know,

Heron's formula :

Area of triangle = √s(s - a)(s - b)(s - c)

[Where, s is semi-perimeter a, b and c are sides of triangle]

So,

→ s = Perimeter of triangle/2

→ s = 8 + 8 + 8/2

→ s = 24/2

→ s = 12

Perimeter of triangle is 24 cm.

Semi-perimeter is 12 cm.

Then,

→ Area = √12(12 - 8)(12 - 8)(12 - 8)

→ Area = √12 × 4 × 4 × 4

→ Area = √2 × 2 × 3 × 2 × 2 × 2 × 2 × 2 × 2

→ Area = 2 × 2 × 2 × 2 × √3

→ Area = 16√3

Area of triangle is 16√3 cm².

Now,

We also know,

Area of triangle = 1/2 × base × height

→ 16√3 = 1/2 × 8 × height

→ Height = (16√3 × 2)/8

→ Height = 32√3/8

→ Height = 4√3

Thus,

Height of triangle is 4√3 cm.