What is the area and perimeter of an equilateral triangle with height 2?

1 Answer
George C.
Mar 18, 2016

#"area" = (4sqrt(3))/3#

#"perimeter" = 4sqrt(3)#

Explanation:

If you bisect an equilateral triangle with sides of length #2x#, then you get two right angled triangles with sides of length #2x#, #x# and #sqrt(3)x#, where #sqrt(3)x# is the height of the triangle.

In our case, #sqrt(3)x = 2#, so #x = 2/sqrt(3) = (2sqrt(3))/3#

The area of the triangle is:

#1/2 xx base xx height = 1/2 xx 2x xx 2 = 2x = (4sqrt(3))/3#

The perimeter of the triangle is:

#3 xx 2x = 6x = (12 sqrt(3))/3 = 4sqrt(3)#

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