How doy ou find the area of an equilateral triangle inscribed in a circle with a circumference of 64(pi) cm?

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Answer 1 · 2015-06-01T11:36:28

If the circumference of a circle is $64pi$ cm. then it's diameter is $64$ cm. (since circumference $= 2 *$ diameter).

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Based on the diagram (above).

The sides of this equilateral triangle have a length of
$s=cos(30^@)*64$
$color(white)("XXXXX")$ and since $cos(30^@) = sqrt(3)/2$
$= 32sqrt(3)$

The height of the equilateral triangle is
$h = cos(30^@) * s$

$= sqrt(3)/2* 32sqrt(3)$

$=48$

The area of the equilateral triangle is
$A= 1/2sh$

$= 1/2*32sqrt(3)*48$

$=768sqrt(3)$