The term “parallelogram” originates from the Greek word “parallelogrammon,” which means “bounded by parallel lines.” The English word “parallelogram” indicates the same thing. Consequently, a parallelogram is a name given to a quadrilateral that has parallel lines serving as its boundaries. Both of this form’s opposing sides are parallel to one another and are of identical length. There are three basic types of parallelograms: square, rectangle, and rhombus, and each of them has its own set of distinguishing properties.
So what is a parallelogram shape? In this section, in addition to the questions that have been addressed, we will acquire knowledge on parallelograms and the manner in which their areas as well as other pertinent issues may be determined.
On this website, we offer thousands of free printable worksheet collections to help you thoroughly prepare for teaching.
What is a Parallelogram shape?
A parallelogram is a special sort of quadrilateral that is formed by connecting lines that are parallel to one another. A parallelogram may have any angle between its adjacent sides, but in order for it to be considered a parallelogram, the sides that are perpendicular to one another must be parallel.
A parallelogram is formed when the diagonals of two opposing sides of a quadrilateral are both parallel and congruent to one another. Consequently, a parallelogram is a name given to a quadrilateral in which both sets of opposing sides are parallel to one another and equal to one another.
Parallelogram properties
In the parallelogram:
- Opposite sides are equal
- Opposite angles are equal
- The midpoint of each line is where two diagonals come together.
Signs to Recognize Parallelograms
The parallelogram identification signs are the factors that help you prove a quadrilateral is a parallelogram. Signs of parallelograms include:
- A quadrilateral with opposite sides/equal opposite sides parallel is a parallelogram
- A quadrilateral with equal opposite angles is a parallelogram
- A quadrilateral with two diagonals intersecting at the midpoint of each is a parallelogram
Calculating the Perimeter of a Parallelogram
The perimeter of a parallelogram is 2 times the sum of any pair of adjacent sides. In other words, the perimeter of the square is the sum of the lengths of the four sides of the parallelogram.
The detailed formula to calculate the perimeter of a parallelogram is as follows:
Formula: C = (a+b) × 2
In there:
- C: Perimeter of a parallelogram
- a and b: Any two sides of a parallelogram
Example: Given a parallelogram ABCD with sides a and b of 5 cm and 7 cm respectively. What is the perimeter of the mentioned parallelogram?
Applying the formula for the perimeter of a parallelogram, we have:
C = (a +b) × 2 = (7 + 5) × 2 =12 × 2 = 24 cm
Calculating the Area of a Parallelogram
The area of a parallelogram is measured by the size of its surface, which is the visible plane part of the parallelogram. The area of a parallelogram is calculated as the product of the base times the height.
Formula: S = a × h
In there:
- a: base side of the parallelogram
- h: height (joint from top to bottom of a parallelogram)
Example: There is a parallelogram whose base length CD = 2cm and the height joining from vertex A to side CD is 3cm long. What is the area of the mentioned parallelogram?
The formula for calculating the area of a parallelogram, we apply it to calculate the area of a parallelogram as follows:
The length of the bottom edge CD (a) is 8 cm and the connecting height from the top to the bottom edge is 5 cm. So we have a way to calculate the area of a parallelogram:
S (ABCD) = a × h = 2 × 3= 6 cm2
Calculate the Area of a Parallelogram with Two Diagonals
Usually, if the problem only gives one piece of data about the lengths of two diagonals, we probably won’t be able to solve it. Therefore, the problem will often give the angle between the two accompanying diagonals. As follows:
Given a parallelogram ABCD with diagonals AC and BD, the intersection of the two diagonals is O, and the measure of the angle AOB is formed by the two diagonals. The area of a parallelogram when the lengths of the two diagonals are known is calculated as follows:
S = 1/2×AC×BD×Sin(AOB) = 1/2×AC×BD×Sin(AOD)
The general formula for calculating the area of a parallelogram when two diagonals are known is S = 1/2×c×d.sinα
With:
- c, d are the lengths of the two parallelogram diagonals (same unit of measure) respectively.
- α is the angle formed by the two diagonals.
Special Parallelogram Shapes
Rhombus
In the context of Euclidean geometry, a quadrilateral with four equal sides is referred to as a rhombus. This is either a parallelogram with two adjacent sides that are congruent with each other or a parallelogram with two diagonals that are perpendicular to each other.
Below are the properties of a rhombus:
- The two diagonals are the angle bisectors of the rhombus
- A rhombus has equal opposite angles, the sum of the angles in a rhombus is 360 degrees
- Two diagonals are perpendicular and intersect at the midpoint of each line
- The two diagonals are the bisectors of the angles in the rhombus
Rhombus identification sign
- A parallelogram has two congruent adjacent sides
- A parallelogram has two diagonals that are perpendicular to each other
- A parallelogram whose diagonal is the bisector of an angle
The detailed formula to calculate the perimeter of a rhombus is as follows:
The area of a rhombus is measured by the size of its surface. Is the plane part we can see of the rhombus. The area of a rhombus is half the product of the lengths of the two diagonals, with the following formula: Sabcd = (d1Xd2). In there S is the area of the rhombus while D1/D2 are the two diagonals of the rhombus.
The formula for the area of a rhombus
The perimeter of a rhombus is calculated as the sum of the lengths of the lines surrounding the figure. It is also the road that encloses the entire area. To calculate the perimeter of a rhombus, we take the sum of the lengths of 4 sides, the formula is the same: P = a × 4. In there:
- P: is the circumference of the circle.
- a: is the length of each side of the rhombus.
Square
In Euclidean geometry, a square is an equilateral quadrilateral, that is, with 4 equal sides and 4 equal angles (4 right angles). A square can be conceptualized as a rhombus with two equal diagonals or as a rectangle with equal sides. A square is also a special form of a parallelogram.
The Cartesian coordinates of the vertices of a square centered at the origin and 2 units long, parallel to the coordinate axes are (±1, ±1). The interior of that square includes all points (x0, x1) with -1 < xi < 1.
Properties of squares
- The two diagonals are equal, perpendicular, and intersect at the midpoint of each.
- The intersection of the two diagonals of a square is the center of the circumscribed and inscribed circles.
- The intersection of bisectors, medians, and orthogonal all coincide at a point.
- A diagonal line divides the square into two equal areas.
- There is an inscribed and circumscribed circle, and the centers of both circles coincide and are the intersection of the diagonals of the square.
- A square is a two-dimensional shape that shares characteristics with both a rectangle and a rhombus.
Square identification signs
- A rectangle with two equal adjacent sides/perpendicular diagonals is a square.
- A rectangle whose diagonal is the bisector of an angle is a square.
- A rhombus with two equal diagonals is a square.
Rectangle
A rectangle in Elucid geometry is a quadrilateral with four right angles. With this definition, we see that a rectangle is a convex quadrilateral with four right angles or a parallelogram with one right angle.
The rectangle is so named because it resembles the Japanese characters of Chinese characters. A rectangle is a quadrilateral with three right angles, an isosceles trapezoid with one right angle, a parallelogram with one right angle or a parallelogram with two equal diagonals is a rectangle.
Rectangle properties
- Rectangles have most of the properties of parallelograms and isosceles trapezoids
- The two diagonals of the rectangle intersect and are equal at the midpoint of each line, and form 4 isosceles triangles.
- Inscribed in a circle whose center is the center of the figure.
Rectangular identification signs
To be able to recognize a rectangle, people can rely on the following characteristics:
- A quadrilateral with three right angles is a rectangle.
- An isosceles trapezoid with one right angle is a rectangle.
- A parallelogram with a right angle/ two equal diagonals is a rectangle.
The formula for the perimeter of a rectangle
The perimeter of the rectangle is calculated by the sum of the lengths of the lines surrounding the figure, which is also the line that encloses the entire area. The area of a rectangle has a perimeter that is equal to two times the total of its length and width.
Formula: P = (a + b ) × 2
We have: a is the width of the rectangle, b is the length of the rectangle, and P is the perimeter of the rectangle.
Final Words
What is a parallelogram shape? Above are the definition, formulas, properties, and how to recognize a parallelogram. Hope the above article can help you in solving these kinds of math exercises. If you are planning to teach your kids about this essential topic, you can make your own collections of parallelogram worksheets using our worksheet generator. Good luck!
