How do we find the area of a rhombus ?

2 Answers
May 2, 2018

#A=1/2L_1L_2# where #L_1# and #L_2# are the diagonal lengths of the rhombus.

Explanation:

#A=1/2L_1L_2# where #L_1# and #L_2# are the diagonal lengths of the rhombus - The rhombus can be visualized as #2# congruent triangles with one of the diagonals being a shared side. Because each of a rhombus's diagonals perpendicularly bisect the other, the opposite bisector represents the height of the each triangle. The formula for area of a triangle is #1/2bh#, or in this case #1/2L_1(1/2L_2)#. Since there are 2 of these triangles in a rhombus, the equation for area of a rhombus is:
#2*1/2L_1(1/2L_2)#, which simplifies to:
#A=1/2L_1L_2#

May 2, 2018

As below.

Explanation:

enter image source here

https://www.google.co.in/search?biw=1680&bih=919&tbm=isch&sa=1&ei=FCzpWqSnGozmvgTe4LCoBg&q=rhombus+area+formula&oq=rhombus+area&gs_l=psy-ab.1.1.0l10.1256997.1260186.0.1262529.12.10.0.2.2.0.164.1296.0j10.10.0....0...1c.1.64.psy-ab..0.12.1308...0i67k1.0.TyntobIUlys#imgrc=_

#color(maroon)("Case 1 : Known diagonals :-"#
#"Area of Rhombus " = A = (1/2) * d_1 * d_2, " where " d_1, d_2 " are the diagonals"#

#color(maroon)("Case 2 : Known side and interior angle :-"#
#"Area of Rhombus " = A = a^2 sin theta, " where 'a' is the side and "theta " the interior angle of the rhombus"#

#color(maroon)("Case 3 : Known side and height :-"#
#"Area of Rhombus " = A = a * h " where 'a' is the side and 'h' the height of the rhombus"#