Question

Each side of a rhombus is 13 CM and one of its diagonal is 10 CM Find the length of its other diagonal and the area of the rhombus

Answer 1

We know, diagonals of rhombus bisects each other at 90°


side² = ( I diagonal / 2 )² + ( II diagonal / 2 )²



=> 13² = ( 10 / 2 )² + ( II diagonal / 2 )²

=> 169 = 25 + ( II diagonal / 2 )²

=> 2 √144 = II diagonal

=> 24 = II diagonal : Answer 1




Area = half of product of diagonals

Area = 10 × 24 × 1/2

Area = 10 × 12

Area = 120 cm²



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Answer 2

Heya !!



Let ABCD is a rhombus.




In which,



AD and BC are its two diagonals.



AB = AC = CD = BD = 13 cm




Let ,



AD = 10 cm



OA = AD/2 = 5 cm .






In right angled triangle OAB,



OB² = (13)² - (5)²





OB² = 144



OB = root 144 = 12 cm




BC = 2 × OB = 2 × 12 = 24 cm



Therefore,



Area of rhombus ABCD = 1/2 × ( AD × BC )




=> 1/2 × ( 10 × 24 )


=> 240/2



=> 120 cm²