Input Data :
Length of Rhombus = 10 in
Angle = 30
Objective :
Find the perimeter of rhombus?
Formula
Area (Trigonometry) = A2 sinθ
Perimeter = 4 x Angle
Solution :
Area = 102 x sin(30)
= 100 x 0.5
Area = 50 in²
Perimeter = 4 x 30
Perimeter = 120 in
Area & Perimeter of Rhombus calculator uses side length and the measure of an angle or the lengths of diagonals of a rhombus, and calculates the perimeter and area of the rhombus. It is an online Geometry tool requires side length and measure of the angle or lengths of diagonals of a rhombus. Using this calculator, we will understand the trigonometric and diagonal method for finding the perimeter and area of a rhombus.
It is necessary to follow the next steps:
A quadrilateral with four congruent sides is a rhombus or diamond (see the picture below). In some literature it is named equilateral quadrilateral, since all of its sides are equal in length.
That means, if ${\overline{AB}}\cong{\overline{BC}}\cong{\overline{CD}}\cong{\overline{DA}}$, then ${\overline{ABCD}}$ is a rhombus. Since opposite sides are parallel, the rhombus is a parallelogram, but not every parallelogram is a rhombus. That means that all the properties of a parallelogram can be also applied to rhombus. To recall, the parallelogram has the following properties:Calculating areas and perimeters of various geometrical figures are very useful in mathematics as well as in real life problems.
Rhombus often appear in real life. For instance, a square box, a cracker, a kite, a diamond, a pencil eraser are examples of rhombus.
In three-dimensional geometry, problems with prism and pyramid with rhombus bases very often appear. There is another interesting solid with rhombus bases, the so-called rhombic triacontahedron. It is the thirty-faced convex polyhedron with $30$ rhombic sides.
Practice Problem 1:
A rhombus has a perimeter of $60$ centimeters and the length of one diagonal is $16$ centimeters. Find its area.
Practice Problem 2:
If base angle of a rhombus measures $60$ degrees and the length of the side of the rhombus is $10\;in$, find its perimeter and area.
The Rhombus calculator, formula, example calculation (work with steps), real world problems and practice problems would be very useful for grade school students (K-12 education) to understand the concept of perimeter and area of rhombus. This concept can be of significance in geometry, to find the perimeter and area of complex figures, as well as to find surface area and volume of some solids.