If the height of an equilateral triangle is 5.382 inches, what is its area?

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If the height of an equilateral triangle is 5.382 inches, what is its area?

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Answer 1 · 2015-12-09T08:50:08

$\times x 9.655308 \cdot \sqrt{3}$ $color(white)(xxx)9.655308*sqrt3$

Explanation:

Let a be length of one side of the triangle:

$\times \sqrt{3} \cdot \frac{a}{2} = h$ $color(white)(xx)sqrt3*a/2=h$
$\Rightarrow \sqrt{3} \cdot \frac{a}{2} = 5.382$ $=>sqrt3*a/2=5.382$
Multiply both side by $\frac{2}{\sqrt{3}}$ $2/sqrt3$
$\times \frac{2}{\sqrt{3}} \cdot \sqrt{3} \cdot \frac{a}{2} = \frac{2}{\sqrt{3}} \cdot 5.382$ $color(white)(xx)color(red)(2/sqrt3*)sqrt3*a/2=color(red)(2/sqrt3*)5.382$

$\Rightarrow a = 5.382 \cdot \frac{2}{\sqrt{3}}$ $=>a=5.382*2/sqrt3$
Multiply both numerator and denominator by $\sqrt{3}$ $sqrt3$
$\times x = 5.382 \cdot \frac{2}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}}$ $color(white)(xxx)=5.382*2/sqrt3color(blue)(*sqrt3/sqrt3)$
$\times x = 2 \cdot 1.794 \sqrt{3}$ $color(white)(xxx)=2*1.794sqrt3$

$\times A = a \frac{h}{2}$ $color(white)(xx)A=ah/2$
$\times x = 2 \cdot 1.794 \cdot \sqrt{3} \cdot 5.382 \cdot \frac{1}{2}$ $color(white)(xxx)=2*1.794*sqrt3*5.382*1/2$
$\times x = 9.655308 \cdot \sqrt{3}$ $color(white)(xxx)=9.655308*sqrt3$

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If the height of an equilateral triangle is 5.382 inches, what is its area?

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