The diagonals of a rhombus are 20 cm and 16 cm. Find its area, length of
its sides and perimeter.
Answers
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Step-by-step explanation:
The area of rhombus is A=160\ cm^2A=160 cm
2
The length of the side of the rhombus is s=2\sqrt{41}\ cms=2
41
cm
The perimeter of rhombus is P=8\sqrt{41}P=8
41
Step-by-step explanation:
Given : The diagonals of a rhombus are 20 cm and 16 cm.
To find : Its area, length of its sides and perimeter ?
Solution :
The diagonal of rhombus is
d_1=20,\ d_2=16d
1
=20, d
2
=16
The area of rhombus is A=\frac{1}{2}(d_1\times d_2)A=
2
1
(d
1
×d
2
)
A=\frac{1}{2}(20\times 16)A=
2
1
(20×16)
A=\frac{1}{2}(320)A=
2
1
(320)
A=160\ cm^2A=160 cm
2
The length of the side of the rhombus is s=\sqrt{(\frac{d_1}{2})^2+(\frac{d_2}{2})^2}s=
(
2
d
1
)
2
+(
2
d
2
)
2
s=\sqrt{(\frac{20}{2})^2+(\frac{16}{2})^2}s=
(
2
20
)
2
+(
2
16
)
2
s=\sqrt{(10)^2+(8)^2}s=
(10)
2
+(8)
2
s=\sqrt{100+64}s=
100+64
s=\sqrt{164}s=
164
s=2\sqrt{41}\ cms=2
41
cm
The perimeter of rhombus is P=2\sqrt{d_1^2+d_2^2}P=2
d
1
2
+d
2
2
P=2\sqrt{20^2+16^2}P=2
20
2
+16
2
P=2\sqrt{400+256}P=2
400+256
P=2\sqrt{656}P=2
656
P=2\times 4\sqrt{41}P=2×4
41
P=8\sqrt{41}P=8
41
#Learn more
In a rhombus diagonals of a rhombus are ---- in length
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