What is the area of an equilateral triangle with a side of 8?

3 Answers

The area of a equilateral triangle with sides a is

#A=sqrt3/4*a^2=>A=sqrt3/4*(8)^2=27.71#

Nov 25, 2015

Area equals to #16sqrt(3)#

Explanation:

Consider an equilateral triangle #Delta ABC#:
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The area of this triangle is
#S=1/2*b*h#

All its sides are given and equal to #8#:
#a=b=c=8#,
its altitude #h# is not given, but can be calculated

Let the base of the altitude from vertex #B# to side #AC# be point #P#. Consider two right triangles #Delta ABP# and #Delta CBP#. They are congruent by a common cathetus #BP# and congruent hypotenuses #AB=c=BC=a#.
Therefore, the other pair of catheti, #AP# and #CP# are congruent as well:
#AP=CP=b/2#

Now the altitude #BP=h# can be calculated from the Pythagorean Theorem applied to a right triangle #Delta ABP#:
#c^2 = h^2 + (b/2)^2#
from which
#h=sqrt(c^2-(b/2)^2)=sqrt(64-16)=4sqrt(3)#

Now the area of triangle #Delta ABC# can be determined:
#S=1/2*8*4sqrt(3)=16sqrt(3)#

Nov 25, 2015

16#sqrt#3

Explanation:

Area of equilateral triangle = #sqrt3 a^2#/4
In this situation,
Area = #sqrt3*8^2#/4
= #sqrt3*64#/4
= #sqrt3*16#
= 16#sqrt3# sq. unit