Question

Each side of a rhombus is 20 cm long and one of its diagonals is 24 cm in length, find the area of ​​this rhombus?

please help me on this ​

Answer 1

Given :

• Side of rhombus = 20 cm

• Diagonal_1 of rhombus = 24 cm

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To find :

• Diagonal_2 of rhombus

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Note :

Kindly keep in touch with picture

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Solution:

We know:

`\bigstar \boxed{ \rm Area = (Diagonal_1 * Diagonal_2 )/(2)}`

As we can clearly see we need both diagonals, but in question only one diagonal is given.

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So first let's find other diagonal.

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`\red{\textsf{ \textbf{To find Diagonal}}} \red{\sf\pmb{_2}} \leadsto`

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In △ AOB :

AB - Hypotenuse

AO = Perpendicular

BO = Base

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Base² = Hypotenuse ² - Perpendicular²

∴ BO² = AB² - AO²

• BO² = 20² - 12²
• BO² = 400 - 12²
• BO² = 400 - 144
• BO² = 256
• BO = √(256)
• BO = √(16 × 16)
• BO = 16 cm²

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• Diagonal_2 = 2BO
• Diagonal_2 = 2 × 16
• Diagonal_2 = 32 cm

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`\red{\textsf{ \textbf{To find Area}}} \leadsto`

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As we already know Area of rhombus so :

`\twoheadrightarrow\sf Area = (Diagonal_1 * Diagonal_2 )/(2) \\`

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`\twoheadrightarrow\sf Area = (32 * 24)/(2) \\`

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`\twoheadrightarrow\sf Area = (768)/(2) \\`

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`\twoheadrightarrow\bf Area = \red {384 {cm}^(2) } \\`