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Maths / Mensuration / Area of Rhombus
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Area of Rhombus

Rhombus: quadrilateral all of whose sides have the same length.

Area of Rhombus: A rhombus is actually just a special type of parallelogram. The "base times height" method: First pick one side to be the base. Any one will do, they are all the same length. Then determine the altitude - the perpendicular distance from the chosen base to the opposite side. The area is the product of these two, or, as a formula: Area = base x height:.

The "diagonals" method: Another simple formula for the area of a rhombus when you know the lengths of the diagonals. The area is half the product of the diagonals. As a formula: Area =frac{1}{2} times d_1times d_2  where, d1 is the length of a diagonal and d2 is the length of the other diagonal

ExampleFind the area of a rhombus having each side equal to 13 cm  and  one of whose deiagonals is 24 cm.

Solution :  Let ABCD be the given parallelogram whose diagonals intersect  at  O. We have,  AB = 13 cm and  AC = 24 cm. Since the diagonals of a rhombus bisect each other at right angles. Therefore, large Delta AOB is a right triangle, right angled at O such that  large OA = frac{1}{2} AC =12 cm   and AB = 13cm.

Using Pythagoras theorem, in large Delta AOB, we have large ^{AB^{2}  =  large ^{OA^{2}+ large ^{OB^{2}   large Rightarrow large ^{13^{2}}   =  large ^{12^{2}} + large ^{OB^{2}}  large Rightarrow large ^{OB^{2}}   =  large ^{13^{2}} - large ^{12^{2}}large Rightarrow large ^{OB^{2}}  = 169 - 144 = 25   large Rightarrow large ^{OB^{2}}   =  large ^{5^{2}}

Hence,  OB = 5 cm  Also, BD = 2 x OB = 10cm

Hence , Area of rhombus ABCD = large frac{1}{2}times ACtimes BD   = frac{1}{2}times 24times 10 cm^{2}=120cm^2


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