Question

The sides of a rhombus are 10 cm each and a diagonal measures 16 cm. Find the area of the rhombus.


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Answer 1

Let’s take Triangle ABO (I am considering AC = 16 cm)

AB = 10 cm is the hypotenuse

AO = 8 cm (half of AC as diagonals bisect)

hence in the triangle ABO , using Pythagorean theorem ,

[math]AO^2 + BO^2 = AB^2[/math]

[math]BO^2 + 8^2 = 10^2[/math]

[math]BO^2 +64 = 100[/math]

[math]BO^2 = 100 - 64 ==> 36[/math]

[math]√(BO^2) = √36[/math]

BO = 6 cm

therefore diagonal [math]BD = 2 * BO[/math]

BD = 12 cm

hence area of rhombus = 1/2 * AC * BD

[math][1/2 * ( 16 * 12 ) ]cm^ 2[/math]

96 cm^2 ans

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Answer 2

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