# Area Of A Rhombus | Geometry Formulae

# What Is The Area Of A Rhombus, And How Does It Compare To Rectangles?

The area is the space an object takes up. A rectangular prism has two dimensions of the length and one dimension of height or width. A rhombistepramid also has two dimensions of length, but it also has a dimension that is the sum of the sizes of its diagonals. The dimensions of a rhombus can be calculated by multiplying its height by its width. For example, consider a rhombus with a length of 10 cm and a width of 5 cm. This rhombus has an area of (10 × 5) = 50 cm2.

Perimeter is the distance around a polygon or other closed shape. The perimeter of any polygon can be estimated by adding its sides together. For example, if we were to calculate the perimeter of an equilateral triangle with a base length of 8 m, we would need to add two lengths together (see Figure 1). Perimeter = 2(8 m) + 2(8 m) = 24 m.

## Geometry Formulae

The following information is provided in geometry formulae and can be useful when solving problems. Equilateral triangle: All sides equal, each angle equal to 60°, one side is a diameter of a circle with that base length. Right-angled triangle: One angle is 90°, one side is a circle’s diameter with that base length. Trapezium: All sides are equal, all angles are equal to 120°. Regular polygon: The same number of sides as angles around the polygon and the same number of interior angles as exterior angles (an ‘exterior’ side). Circle:

Radius=diameter(diameter=2r)Circumference = 2πrHeight=a/2Perimeter = 2πrSince radius and diameter are used interchangeably, if the diameter is four times the radius, then r=4a.Ex: Two sides are 8cm and 12 cm. Find the perimeter and height.Given that height=a/2Height = 16/2=8Height = 4cmCircumference = 2πrCircumference = 2π(12)circumference = 144cmPerimeter = 2πrPerimeter = 2(8)(12)perimeter = 32 + 48perimeter = 80cm true Ex: Find the perimeter and height of a square with a flank length of 6 cm. Perimeter = 2πrPERIMETER = 2π(6)PERIMETER = 12+12PERIMETER = 24Height = a/2Height = (1/2)(6)= 3cmThe formula for finding the area of different shapes is different.

### What is a Rhombus?

A rhombus is a shape that has four sides of equal length and two sets of opposite parallel and perpendicular sides. On the other hand, a rectangle is a shape with four right angles. A rhombus has two parallel and perpendicular lines, while a rectangle only has one set. The rhombus is similar to an equilateral triangle. However, the rhombus has different sides of equal length. Most books will refer to a rhombus as a parallelogram.

### Rhombus Definition

A Rhombus has four congruent sides and diagonals perpendicular to each other. The opposite angles formed by this shape are equal, while the adjacent angles are equal but not congruent. It is a type of parallelogram with equal sides, which are all parallelograms. These properties make it a parallelogram but not a rectangle. Rhombi are used in many shapes and other geometric forms whether they have the exact dimensions.

For example, a rhombus may describe a parallelogram with an oblique angle different from the two acute angles that form it. The term rhombus can also be used for a rectangle that does not have right angles as long as it has an oblique angle.

For a rhombus with sides of length (ignoring direction), a = b = c, and for an oblique rhombus, a < b < c; the straddling sides are. If drawn, a parallelogram can be turned into a rhombus so that both pairs of parallel opposite sides are rotated. In a rhombus, opposite angles are supplementary and congruent to one another.

## The Area of a Rhombus

A rhombus is a parallelogram with four matching sides and angles. It has the same properties as a rectangle but the opposite properties. The area of a rhombus is calculated by multiplying the length of one side by the length of another side to get the total area. The formula is: Area = s(s-a), where s is the length of one side and a is the length of the other side.

For example, if a rhombus has sides measuring four units in length, its area would be 16 units square. If one side measures five units, then another must measure three units for the area to remain constant at 16 units square.

Area = 4(3) = 16 true Area = 5(3) = 15 false therefore, the answer is B, area of the rhombus is not conserved.A rectangle with sides 3 and 4 has a perimeter of 12. A rectangle with sides 6 and 8 has a perimeter of 24. Use this information and your knowledge of rectangles to determine the length and width of each rectangle to have all four values equal. Area = 2lwPerimeter = 2(l+w)From the first answer,

we know that the side of the bigger rectangle is 6. Since it has a perimeter of 24, its width must be 12. The other side of this rectangle is 8, and its area is 16, so l = 4. From the second answer, we know that the side of the smaller rectangle is 3. Since it has a perimeter of 12, its width must be 6. The other side of this rectangle is 4, and its area is 9, so w = 3.

### Calculating The Area of A Rectangle Without Measurement

A rectangle is a squarish shape that has four sides. A rhombus is a parallelogram with four sides. The area of a rectangle cannot be calculated without the measurements of each side.

To figure out the area of a rhombus, use the following formula: Area = Length x Width. Find out how to measure the area of a rectangle or rhombus with these steps.

Area = Length x Width = (Length x 2) + Length = 2xL + L = 2xL + L = 2xL + L = 4xL

Calculating The Area of A Rectangle Without Measurement Step 1: Determine if the object is a rectangle. The easiest way to determine if you have a rectangle is by drawing diagonal lines across each side. Step 2: If the object is a rectangle, measure the length and width of two opposing sides of the rectangle. Step 3: Calculate the area by multiplying the length times itself. If you’re trying to figure out the area of a rhombus, multiply both lengths by themselves. . Easy!

How to estimate the area of a rectangle using mathematical formulas? Do we need to find out any other information? How to estimate the area of a rectangle without measuring it? How to estimate the dimensions of a rectangle without measuring it? Skip navigation…How To: Calculate a Room’s Square Footage for HVAC Duct Work by Measuring the Room’s Dimensions. How To Measure Length and Area of Rectangular Objects with a Calculator (Part 2). Step 1: Measure the length and width of your rectangle.

### How to Compute the Area of a Rhombus

To calculate the area of a rhombus:

- Draw an X in the middle of the shape.
- Divide one side of the X by two, and use that number as the base for your calculation.
- Multiply this number by itself (the base) to get the area.

To determine if a rhombus has more or less area than a rectangle, you must measure them both. If a rhombus has an area higher than a rectangle with the same length and width, it has more area. If it has less, then it has less. To find out how much less or more, subtract the rhombus area from the rectangle area. To understand how to calculate the volume of a rhombus, read through our article on calculating the volume of a cylinder.

#### Conclusions

The area of a rhombus is three times the length of the width. This is the same as a rectangle that’s cut into thirds. The area of a parallelogram is its height times the width. The dimensions of a triangle are 1/2 its base times the height.

The height of a square pyramid is 1/3 its side length, so the volume is (1/2)(side length)(height).

The more sides something has, the more pieces can be made. This one’s fun – even something as dull as a box has more than one way to cut it into pieces. The dimensions of a rectangle are the product of its length and width, A=L*W. The measurement of any parallelogram is base times height, A=b*h. The area of an equilateral triangle is 1/2 base times height, A=1/2b*h.

### What is the area of a rhombus?

A rhombus is a parallelogram because it has two pairs of parallel, non-opposite sides. It is characterized by four equal-length sides and four acute angles. The area of a rhombus is calculated by multiplying the length of one side by the length of another side, then taking half that amount. This equals formula A=l x w/2, where l and w are the lengths of the two opposite sides. What are the dimensions of an equilateral triangle?

An equilateral triangle has three equal sides and three 60° angles. The dimensions of an equilateral triangle are calculated by multiplying the length of anyone’s side by ½ (0.5). This equals formula A=s x 0.5, where s is the length of aside.

What are the dimensions of an acute triangle?. An acute triangle has three angles that are less than 90 degrees. An acute triangle has only one main diagonal. The dimensions of a critical triangle are calculated by multiplying the length of the base by 1/2 (0.5) on both sides and then multiplying that sum by the altitude to get a final answer. This equals formula A=b x 0.5 x h, where b is the length of the base and the altitude of an acute triangle. What is the area of a right triangle?.

### How do you count the dimensions of a rhombus?

The area of a rhombus is calculated by the length of its opposite side multiplied by the length of its adjacent side. For example, if the length of the opposite side is 4 inches and the length of the adjacent side is 6 inches, then the area would be 4*6 = 24 square inches. If you are given the measurement of one side and the area of the rhombus, then you may use these formulas to find out the length of the other two sides: S2 = a2 + b2 – 2ab Cosine(A) = a/b 45-45-90 Rhombus Theorem. This theorem is also called Heron’s Formula, which states that if QPR is a square and OP=OS=a, PQ=PR.

**Proof:** QPR is a square whose sides are equal, so each of the opposite sides is equal to each of the adjacent sides. This means that SR = SQ = r and OP = OS = a. Then p2 + q2 – 2(pq/r) = 0

p2 + q2 – 2pq/r = 0 If you use the quadratic equation method, you will have: p2 + q 2 – 2pq/r = 0 (x + y) (x – y) = 0 Then the values of x and y are: x = -1/2 and y = 1. In this case, p=1/2, q=1 and r=a. Therefore: PQ=OP+OS=1/2+a= a If you use determinant method, you will have: S3-S2S1S3-S2S1 S3-S2 S1-S2 S3-S2 S1+S2 S1+S2 So: PQ=a.