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solong [7]
2 years ago
15

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?

Mathematics
2 answers:
Allushta [10]2 years ago
8 0
<h3>Given :</h3>

  • Side of rhombus = 20 cm

  • Diagonal_1 of rhombus = 24 cm

\\  \\

<h3>To find :</h3>
  • Diagonal_2 of rhombus

\\  \\

<h3>Note :</h3>

Kindly keep in touch with picture

\\  \\

<h3>Solution:</h3>

We know:

\bigstar \boxed{ \rm Area = \dfrac{Diagonal_1 \times Diagonal_2 }{2}}

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

\\

So first let's find other diagonal.

\\

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

\\

In △ AOB :

AB - Hypotenuse

AO = Perpendicular

BO = Base

\\

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

\\

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

\\  \\

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

\\

As we already know Area of rhombus so :

\twoheadrightarrow\sf Area = \dfrac{Diagonal_1 \times Diagonal_2 }{2} \\

\\  \\

\twoheadrightarrow\sf Area = \dfrac{32 \times 24}{2} \\

\\  \\

\twoheadrightarrow\sf Area = \dfrac{768}{2} \\

\\  \\

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

vodomira [7]2 years ago
6 0

Answer:

AB = 20 CM

OA = 1

__ × 24 cm

2

= 12 cm

AOB = 90 °

OB² == AB² - OA ²

( {20}^{2} ) - ( {12}^{2} ) \\  = 400 - 144 \\  = 256 \\

ob \:  =  \sqrt{256}  = 16 \\ bd \:  = 2 \times ob \\  = 2 \times 16 \\  = 32cm \:  \\

AREA OF ABCD IS

\frac{1}{2 }  \times ac \times bd \\  =  \frac{1}{2}  \times 24 \times 32 \\ 384cm

hope \: its \: helpful \:  \: to \: you \:

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