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Rhombus calculator
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.
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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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