Question

Prove that the area of isosceles triangle is is equal to root 3 by 4

Answer 1

equilateral triangle.



Draw a line from the vertex to the midpoint of the base.



Cut along this line and move half of the triangle to form a rectangle.



If a is the length of a side of the equilateral triangle and h the height then this rectangle has area

1/2 a h

The triangle below, which is half of the rectangle, is a right triangle,



and hence, by Pythagoras' theorem

a2 = h2 + ( a/2)2

Thus h = sqrt( 3/4 a2) = sqrt(3)/2 a. Hence the area of the triangle is

1/2 a h = sqrt(3)/4 a2

Penny