Question

The diagonals of a rhombus are 20 cm and 16 cm. Find its area, length of its sides and perimeter.​

Answer 1

Step-by-step explanation:

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Answer 2

The area of rhombus is $A=160\ cm^2$

The length of the side of the rhombus is $s=2\sqrt{41}\ cm$

The perimeter of rhombus is $P=8\sqrt{41}$

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

$d_1=20,\ d_2=16$

The area of rhombus is $A=\frac{1}{2}(d_1\times d_2)$

$A=\frac{1}{2}(20\times 16)$

$A=\frac{1}{2}(320)$

$A=160\ cm^2$

The length of the side of the rhombus is $s=\sqrt{(\frac{d_1}{2})^2+(\frac{d_2}{2})^2}$

$s=\sqrt{(\frac{20}{2})^2+(\frac{16}{2})^2}$

$s=\sqrt{(10)^2+(8)^2}$

$s=\sqrt{100+64}$

$s=\sqrt{164}$

$s=2\sqrt{41}\ cm$

The perimeter of rhombus is $P=2\sqrt{d_1^2+d_2^2}$

$P=2\sqrt{20^2+16^2}$

$P=2\sqrt{400+256}$

$P=2\sqrt{656}$

$P=2\times 4\sqrt{41}$

$P=8\sqrt{41}$

#Learn more

In a rhombus diagonals of a rhombus are ---- in length

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