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Banking And Insurance

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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 A 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

Example: Find 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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Area of Rhombus

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