Question

Each side of rhombus is 20 cm. Is long, and the length of its 1 diagonal is 24 cm. Find the area of rhombus.​

Answer 1

AnswEr-:

$\underline {\boxed { \mathrm { \red{ Area_{( Rhombus)} = 384cm^{2} }}}}$

Explanation-:

$\mathrm { Given-:}$

• Each side of rhombus is 20 cm .
• Length of its Diagonal¹ is 24 cm

$\mathrm { To\:Find-:}$

• The Area of Rhombus.

$\dag{\mathrm { Solution \:of\:Question-:}}$

$\mathrm { Refer\:the\:Attachment-:}$

• In the Rhombus ABCD .
• AB = 20 cm
• and , AC = 24 cm .

$\mathrm { From\:the\:Attachment-:}$

• AO + CO = 24cm
• Then ,
• AO = 12 cm [ AO = CO ] _________[1]

Now ,

• In $\triangle$ AOB

• AB = 20 cm [ Side of Rhombus]
• AO = 12 cm ________[ From 1 ]

$\mathrm { By\:Applying \:Pythagoras\:Theorem-:}$

• $\star{\mathrm {Hypotenuse^{2} = Base ^{2} + Perpendicular ^{2} }}$

Here,

• AB = 20 cm [ Hypotenuse]
• AO = 12 cm [ Perpendicular]
• BO = ?? [ Base ]

Then ,

• $\longrightarrow{\mathrm {AB^{2} = BO ^{2} + AO ^{2} }}$

Now , By Putting known Values-:

• $\longrightarrow{\mathrm {20^{2} = BO ^{2} + 12^{2} }}$

• $\longrightarrow{\mathrm {BO^{2} = 20 ^{2} + 12^{2} }}$

• $\longrightarrow{\mathrm {BO^{2} = 400 + 144 }}$

• $\longrightarrow{\mathrm {BO = \sqrt{400-144} }}$

• $\longrightarrow{\mathrm {BO = \sqrt {256}}}$

• $\longrightarrow{\mathrm {BO = 16cm }}$

Therefore,

• BO = 16 cm

As , We know that ,

• BO = DO = 16 cm

Then ,

• BD = BO + DO
• BD = 2BO ___[ BO = DO ]
• BD = 16 × 2 [ BO = 16 cm]
• BD = 32 cm

Therefore,

• BD = 16 cm

As ,We , Know that ,

• BD = Diagonal 2 of Rhombus = 32 cm _______[2]

____________________________________________________

As , We know that ,

• $\underline {\boxed { \mathrm { \red{ Area_{( Rhombus)} = \dfrac{1}{2} \times Diagonal 1 \times Diagonal 2 }}}}$

• Here ,
• Diagonal 1 = 24 cm ______[ Given that ]
• Diagonal 2 = 32 cm _______[ From 2]

Now , Putting known Values-:

• $\longrightarrow {\mathrm { \dfrac{1}{2} \times 24 \times 32 }}$

• $\longrightarrow {\mathrm { \dfrac{1}{\cancel{2}} \times \cancel {24} \times 32 }}$

• $\longrightarrow {\mathrm { 12 \times 32 }}$

• $\longrightarrow {\mathrm { Area \:= 384cm^{2} }}$

Hence ,

• $\underline {\boxed { \mathrm { \red{ Area_{( Rhombus)} = 384cm^{2} }}}}$

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