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What is the area of an equilateral triangle that has a perimeter of 18 centimeters?

1 Answer

Jan 26, 2016

Area $= 9 \sqrt{3}$ $= 9sqrt(3)$ sq. cm.

Explanation:

If the perimeter of an equilateral triangle is $18$ $18$ centimeters
$XXX$ $color(white)("XXX")$ each side is $6$ $6$ centimeters long
and
$XXX$ $color(white)("XXX")$ the semi-perimeter, $s$ $s$ , is $9$ $9$ centimeters long.

Using Heron's formula With sides $a = b = c = 6$ $a=b=c=6$ and $s = 9$ $s=9$
$XXX {Area}_{△} = \sqrt{s (s - a) (s - b) (s - c)}$ $color(white)("XXX")"Area"_triangle = sqrt(s(s-a)(s-b)(s-c))$

$XXXXXXX = \sqrt{9 \times 3 \times 3 \times 3}$ $color(white)("XXXXXXX")=sqrt(9xx3xx3xx3)$

$XXXXXXX = 9 \sqrt{3}$ $color(white)("XXXXXXX") = 9sqrt(3)$

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