What is the area and perimeter of an equilateral triangle with height 2?

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What is the area and perimeter of an equilateral triangle with height 2?

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Answer 1 · 2016-03-18T20:50:29

$area = \frac{4 \sqrt{3}}{3}$ $"area" = (4sqrt(3))/3$

$perimeter = 4 \sqrt{3}$ $"perimeter" = 4sqrt(3)$

Explanation:

If you bisect an equilateral triangle with sides of length $2 x$ $2x$ , then you get two right angled triangles with sides of length $2 x$ $2x$ , $x$ $x$ and $\sqrt{3} x$ $sqrt(3)x$ , where $\sqrt{3} x$ $sqrt(3)x$ is the height of the triangle.

In our case, $\sqrt{3} x = 2$ $sqrt(3)x = 2$ , so $x = \frac{2}{\sqrt{3}} = \frac{2 \sqrt{3}}{3}$ $x = 2/sqrt(3) = (2sqrt(3))/3$

The area of the triangle is:

$\frac{1}{2} \times b a s e \times h e i g h t = \frac{1}{2} \times 2 x \times 2 = 2 x = \frac{4 \sqrt{3}}{3}$ $1/2 xx base xx height = 1/2 xx 2x xx 2 = 2x = (4sqrt(3))/3$

The perimeter of the triangle is:

$3 \times 2 x = 6 x = \frac{12 \sqrt{3}}{3} = 4 \sqrt{3}$ $3 xx 2x = 6x = (12 sqrt(3))/3 = 4sqrt(3)$

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What is the area and perimeter of an equilateral triangle with height 2?

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