What is the area of an equilateral triangle, with apothem of 6 inches in length?

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What is the area of an equilateral triangle, with apothem of 6 inches in length?

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Answer 1 · 2015-12-08T13:48:16

$\times 12 \sqrt{3}$ $color(white)(xx)12sqrt3$

Explanation:

$\times \frac{\sqrt{3}}{2} a = h$ $color(white)(xx)sqrt3/2a=h$

$\Rightarrow \frac{\sqrt{3}}{2} a = 6$ $=>sqrt3/2a=6$
$\Rightarrow \frac{2}{\sqrt{3}} \cdot \frac{\sqrt{3}}{2} a = \frac{2}{\sqrt{3}} \cdot 6$ $=>color(red)(2/sqrt3*)sqrt3/2a=color(red)(2/sqrt3*)6$
$\Rightarrow a = \frac{2 \cdot \sqrt{3}}{\sqrt{3} \cdot \sqrt{3}} \cdot 6$ $=>a=(2color(blue)(*sqrt3))/(sqrt3color(blue)(*sqrt3))*6$

$\Rightarrow a = 4 \sqrt{3}$ $=>a=4sqrt3$

$\times A = \frac{a h}{2}$ $color(white)(xx)A=(ah)/2$
$\times \times = 6 \cdot 4 \frac{\sqrt{3}}{2}$ $color(white)(xxxx)=6*4sqrt3/2$
$\times \times = 12 \sqrt{3}$ $color(white)(xxxx)=12sqrt3$

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What is the area of an equilateral triangle, with apothem of 6 inches in length?

1 Answer

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