Question

If the height of an equilateral triangle is 8 cm calculate its area

Answer 1

Hope this will help you ...........

Answer 2

Answer:

The required area of provided equilateral triangle is $\frac{64\sqrt{3}}{{3}}$.

Step-by-step explanation:

Concept:

A triangle is said to be equilateral if each of its three sides is the same length. Equiangular triangles are those with three equal interior angles. The same as an equilateral triangle, an equiangular triangle has three sides that are all equal.

We use the formulas that are given below:

The area of the equilateral triangle $=\frac{\sqrt{3}}{4} *a^{2}$

The height of the equilateral triangle $=\frac{\sqrt{3}}{2} *a$

Given:

The height of the equilateral triangle$= 8 cm$

To find:

We have to find the area of the provided equilateral triangle.

Solution:

As per the question,

$\frac{\sqrt{3}}{2} *a=8$

$a=8*\frac{2}{\sqrt{3}}$

$a=\frac{16}{\sqrt{3}}$ cm

Hence, the area of equilateral triangle is,

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

$=\frac{\sqrt{3}}{4} *\frac{16}{\sqrt{3}}*\frac{16}{\sqrt{3}}$

$=\frac{64\sqrt{3}}{{3}}$

The required area of provided equilateral triangle is $\frac{64\sqrt{3}}{{3}}$.

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