find the area of rombus by herons formula
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Heron's formula is for finding area of a triangle. Rhombus ABCD is a quadrilateral. Divide it into two Δs ABC and BCD.
Length of each side of Rhombus = a
Length of diagonals BD = b and AC = d
we know 4 a² = b² + d²
Semi perimeter of ΔABD or ΔBCD : s = (a+a+b)/2
Area of ABD = Δ = ΔABD + ΔBCD = 2 * Δ ABD
By Heron's formula :
(ΔABD)² = s (s - a) (s -a ) ( s - b)
= (2a+b) (b)(b) (2a - b) /16
= (4 a² - b²) b²/16
= d² b² /16
ΔABD = b d /4
Area of Rhombus = 2 * bd/4 = b d /2
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