Q7 Prove that the area of an equilateral triangle described on one side of a square is equal
to half the area of the equilateral triangle described on one of its diagonals.
Let ABCD be a square of side units.
Therefore, diagonal =
Triangles form on the side and diagonal are ABE and DEF, respectively.
Length of each side of triangle ABE = a units
Length of each side of triangle DEF = units
Both the triangles are equilateral triangles with each angle of .
( By AAA)
Using area theorem,