The sides of rhombus are 10 cm each and a diagonal measures 16 cm. Area of the rhombus is ?
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side of rhombus, a = 10cm
one of diagonal D= 16cm
D/2 = 16/2=8cm
let other diagonal = d
diagonals of rhombus bisect each other right angle. so a right angle triangle is formed with halves of the diagonals and side. using pythagoras theorem
a² = (D/2)² + (d/2)²
⇒ 10² = 8² + (d/2)²
⇒ (d/2) = √(10²-8²) = √36 = 6
⇒ d = 2*6=12cm
Area = Dd/2 = 16*12/2= 96cm²
one of diagonal D= 16cm
D/2 = 16/2=8cm
let other diagonal = d
diagonals of rhombus bisect each other right angle. so a right angle triangle is formed with halves of the diagonals and side. using pythagoras theorem
a² = (D/2)² + (d/2)²
⇒ 10² = 8² + (d/2)²
⇒ (d/2) = √(10²-8²) = √36 = 6
⇒ d = 2*6=12cm
Area = Dd/2 = 16*12/2= 96cm²
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