A rhombus is a parallelogram with four equal and congruent sides, such as a diamond. Squares and rectangles are also types of parallelograms. It is pretty simple to find the height of a rhombus if we already know the other values such as the area, base, or diagonals. Depending on the interior angles, rhombi are sometimes called rectangles or diamonds. Similar to other quadrilaterals, the area of rhombus formula can be applied to calculate the area and other properties of rhombi such as tilt and size when enough information is provided.

Area of a Rhombus

The area of a rhombus is the entire space enclosed within the sides of this four-sided figure. We can apply various formulas to calculate the area of a rhombus based on the information provided. For instance, we can find the area of a rhombus when base- let’s learn about the three ways to calculate the area of a rhombus: With the product of the base and height; with the sin of the angles, or with the product of the diagonals. If the area is known, you can rearrange these same formulas to produce the length of the sides or the perimeter of the shape.

Base-Height Method

To find the area of a rhombus using the base-height method ensure that all of your measurements are in the same units. For example, if the area is square centimeters, the lengths should also be in centimeters.

Example, Divide the area of the rhombus by the height to find the length of one side. For example, if the area is 40 and the height is 4, the quotient of the equation is 10. Multiply the quotient by 4. The product of 10 and 4 is 40. Label the solution with the same unit used for the height. In this case, the solution is 40 inches.

Sin of Angle Method

Write the following formula and plug in the known values to find perimeter i.e., perimeter = 4[area/sin(interior angle)]

Calculate the sin of one of the angles of the rhombus by entering the value into a calculator and pressing the “Sin” key. The adjacent angles within a rhombus are supplementary which means they add up to 180 degrees and have the same sin so it does not matter which angle you use. For example, if the angles are 30 and 150 the sin will be .5 either way. Divide the area by the sin of the angle. For example, if the area is 50 square inches and the angle is 30 degrees, the quotient is 100.

Multiply the quotient by 4 to get the solution, 400. Label the solution with the proper unit measurement, 400 inches.

Diagonal Formula

Find the length of the diagonals: X and Y. If only one diagonal is known, calculate the value of the other diagonal using the following formula: (2 x area)/X = Y. Multiply the area by 2 and then divide it by the known diagonal.

Write down and fill in the following formula with the known information: (1/2X)^2 + (1/2Y)^2 = side^2. If the diagonals are 10 and 20 the formula would read: [(1/2 * 10)^2 + (1/2 * 20)^2 = side^2. Solve the equation starting with the parenthetical phrases and exponents. Ten times .5 is 5. Five squares is 25. Twenty times .5 is 10, squares is 100. Twenty-five plus 100 is 125. The square root of 125 is the value of one side of the rhombus, 11.18.

Multiply the value of one side by 4 to find the perimeter. For example, 11.18 times 4 is 44.72. Label the solution appropriately based on the units of the diagonals.

Understanding the concept of the area of a rhombus is highly crucial for students to attain an in-depth understanding of its various applications. By applying the concepts of the area of the rhombus, they can learn to perform calculations based on the dimensions of this shape. Cuemath offers a wide range of geometry worksheets and math resources designed by math experts to help students learn math with ease.


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