Question

find the area of the equilateral triangle with side 10 centimetre

Answer 1

draw an equilateral triangle
draw the height from the top vertex to the bottom horizontal side
this line segment divides the triangle into two congruent right triangles
this line segment also divides the bottom horizontal side into two congruent line segments, each 5 units in length
the height is the longer leg of the right triangles
taking one right triangle...
the hypotenuse is 10 and the shorter leg is 5
using the Pythagorean Theorem
102=h2+52
100=h2+25
100-25=h2
75=h2
h=√75=√25*3=5√3
A=(1/2)(10)(5√3)
A=(5)(5√3)
A=25√3
A=25*1.732
A=43.3 square units

Answer 2

Area of eqilateral triangle= root3/4×a^2

=root3/4×10^2cm^2
=root3/4×100cm^2
=root3×25cm^2
=25root3cm^2. [Anwser]

Hope it will helpful for you:-)