An equilateral triangle has a height of $\sqrt{6}$ $sqrt(6)$ units. What is the area of the triangle?

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An equilateral triangle has a height of $\sqrt{6}$ $sqrt(6)$ units. What is the area of the triangle?

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Answer 1 · 2018-01-01T13:18:52

Area: $= 2 \sqrt{3}$ $=2sqrt(3)$ sq. units

Explanation:

A common form for the equilateral triangle looks like:
enter image source here
If this common form is scaled up so that the height is $\sqrt{6}$ $sqrt(6)$
then since $\sqrt{6} = \sqrt{3} \times \sqrt{2}$ $sqrt(6)=sqrt(3)xxsqrt(2)$
the scaled up base will have a length of $2 \times \sqrt{2}$ $2 xx sqrt(2)$ (or just $2 \sqrt{2}$ $2sqrt(2)$
(and the height is the given value of $\sqrt{6}$ $sqrt(6)$

The area of this (scaled up) triangle will be:
$Area = \frac{1}{2} \cdot base \cdot height$ $"Area"=1/2 * "base" * "height"$

$XXX = \frac{1}{2} \cdot 2 \sqrt{2} \cdot \sqrt{6}$ $color(white)("XXX")=1/2 * 2sqrt(2) * sqrt(6)$

$XXX = \sqrt{12}$ $color(white)("XXX")=sqrt(12)$

$XXX = 2 \sqrt{3}$ $color(white)("XXX")=2sqrt(3)$

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An equilateral triangle has a height of $\sqrt{6}$ $sqrt(6)$ units. What is the area of the triangle?

1 Answer

Explanation:

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