The diagonal of a rhombus are 26cm and 12cm.find its area and perimeter.
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Let the diagonals of the rhombus be P and Q.
Given ; P = 26 cm and Q = 12 cm.
Area of rhombus =
Area of rhombus = 26 × 12 / 2
Area of rhombus = 312 / 2
Area of rhombus = 156 cm².
Now,
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Let us know first, the properties of rhombus.
1. All sides of a rhombus are equal.
2. Diagonals of a rhombus bisect each other.
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According to question,
AC = 26 cm and BD = 12 cm.
And,
AE = EC = 13 cm.
BE = ED = 6 cm.
[see the above diagram]
Now,
In ΔAED, using pythagoras theorem,
We have ;
AD² = AE² + ED²
AD² = 13² + 6²
AD² = 169 + 36
AD² = 205
AD = √205
AD = 14. 31
As we know,
Each side of a rhombus are equal.
Therefore,
Perimeter = AD + DC + CB + BA
Perimeter = 14.31 × 4
Perimeter ≈ 57. 24 cm
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Thanks for the question!
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Let ABCD be the given rhombus.
We know that the Diagonals of a rhombus are perpendicular bisector of each other. Let the point of intersection of diagonals AC and BD be M.
Given AC = 26 cm and BD = 12 cm
Now, AE = EC/2 = 26/2 = 15 cm
and BE = ED /2 = 12/2 = 6 cm
Now, in right triangle AMD, by pythagoras theorem,
AD2 = AE'2 +ED'2
⇒AD2 =13'2 + 6'2
⇒AD2 =169 + 36 = 205
⇒ AD = √205 =14.31 cm
Again, all the sides of a rhombus are equal.
Therefore, AB = BC = CD = AD = 14.31 x 4 = cm
Now the perimeter of a rhombus = sum of all sides = AB + BC + CD + AD = 14.31cm = 57.24 cm OK
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_____◦•●◉✿[Tʜᴀɴk ʏᴏᴜ]✿◉●•◦_____
●▬▬▬▬▬ஜ۩۞۩ஜ▬▬▬▬▬▬●
______________________________
✔✔✔✔✔✔✔✔✔✔✔✔✔✔✔✔✔✔
Let ABCD be the given rhombus.
We know that the Diagonals of a rhombus are perpendicular bisector of each other. Let the point of intersection of diagonals AC and BD be M.
Given AC = 26 cm and BD = 12 cm
Now, AE = EC/2 = 26/2 = 15 cm
and BE = ED /2 = 12/2 = 6 cm
Now, in right triangle AMD, by pythagoras theorem,
AD2 = AE'2 +ED'2
⇒AD2 =13'2 + 6'2
⇒AD2 =169 + 36 = 205
⇒ AD = √205 =14.31 cm
Again, all the sides of a rhombus are equal.
Therefore, AB = BC = CD = AD = 14.31 x 4 = cm
Now the perimeter of a rhombus = sum of all sides = AB + BC + CD + AD = 14.31cm = 57.24 cm OK
______________________________
❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤
_____________________________
_____◦•●◉✿[Tʜᴀɴk ʏᴏᴜ]✿◉●•◦_____
●▬▬▬▬▬ஜ۩۞۩ஜ▬▬▬▬▬▬●
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