Prove the area of equilateral triangle
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Area of equilateral triangle=√3×a^2/4
area of triangle =1/2×base×height.
In a equilateral triangle draw an atitude from the vertex to the mid point of the opposite side.
now find the length of altitude .
let the side of a triangle be a .
now in half triangle of equilateral triangle .
base =a/2
hypo. =a
perpendicular(altitude)=?
by the phytha.gors. thrm
altitude^2=hypo.^2-base^2
=a^2-a^2/4
=3a^2/4
altitude=√3/2×a
area of triangle =1/2×base×height
=1/2×a×√3/2×a
=√3/4×a^2
hence the area of equilateral triangle=√3/4×a^2,proved
hope it helps u...
Area of equilateral triangle=√3×a^2/4
area of triangle =1/2×base×height.
In a equilateral triangle draw an atitude from the vertex to the mid point of the opposite side.
now find the length of altitude .
let the side of a triangle be a .
now in half triangle of equilateral triangle .
base =a/2
hypo. =a
perpendicular(altitude)=?
by the phytha.gors. thrm
altitude^2=hypo.^2-base^2
=a^2-a^2/4
=3a^2/4
altitude=√3/2×a
area of triangle =1/2×base×height
=1/2×a×√3/2×a
=√3/4×a^2
hence the area of equilateral triangle=√3/4×a^2,proved
hope it helps u...
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Answer:
Step-by-step explanation:area of an equilateral triangle is root 3/4 * side square
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