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Rhombus calculator

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This calculator finds the unknown value of a rhombus given any two known dimensions. The calculator can determine side, area, long diagonal, short diagonal, perimeter, height, incircle radius, and interior angle. The calculator gives you a step-by-step solution on how to find the missing value.

Rhombus Calculator
input two values of a rhombus and select a dimension you want to find
help ↓↓ examples ↓↓
I want to find
Enter values in two text boxes
calculator works with decimals, fractions and square roots (to input $ \color{blue}{\sqrt{2}} $ type $\color{blue}{\text{r2}} $)
side
$ a $ =
 
area
$ A $ =
 
perimeter
$ P $ =
long
diagonal
$ d_1 $ =
 
short
diagonal
$ d_2 $ =
height:
$ h $ =
 
incircle
radius
$ r $ =
angle
$ \alpha $ =
 
angle
$ \beta $ =
working...
Rhombus formulas
$$ A = \frac{d_1 \times d_2}{2} $$
area
$$ A = \frac{a \times h}{2} $$
height
$$ P = 4 \times a $$
perimeter
$$ r = \frac{h}{2} $$
incircle radius
$$ h = a \times \sin\alpha $$
height
$$ \alpha + \beta = 90^o $$
sum of angles
$$ a^2 = \frac{d_1^2}{4} + \frac{d_2^2}{4} $$
side
$$ d_1^2 = 2a^2(1 - \cos\alpha) $$
short diagonal
$$ d_2^2 = 2a^2(1 - \cos\beta) $$
long diagonal
EXAMPLES
example 1:ex 1:
Calculate the perimeter of the rhombus if the diagonals are 16 and 12 centimeters long.
example 2:ex 2:
A rhombus has a circumference of 40 cm and a diagonal of 15 cm. Determine its height.
example 3:ex 3:
A rhombus has a side length of 8 cm, and the angle between the two sides is 45 degrees. Find the radius of the inscribed circle of the rhombus.
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