You probably learned all about plane shapes back in primary school. Triangles, squares, rectangles, circles, those basic 2D shapes we all had to memorize. But now that you’re an adult, have you given much thought to plane shapes and their properties? Maybe not, but they’re all around us, from the rectangular posters on the wall to the circular buttons on your shirt.
In this article, we’ll go beyond just defining plane shapes to looking at their characteristics, types, and common examples you see every day. You may be surprised at how fascinating the world of 2D geometry can be! Stick around as we explore the angles, sides, and secrets of plane shapes.
What Are Plane Shapes? Definition and Overview
A plane shape, also known as a two-dimensional or flat shape, is any shape that can be drawn on a flat surface. Unlike three-dimensional shapes, plane shapes have only two dimensions, length and width. They lack depth or thickness. Plane shapes are two-dimensional figures that have length and width, but no thickness. They are flat shapes that can be measured and calculated using linear dimensions and angles.
Types of Plane Geometric Figures
Triangles
A triangle is a polygon with three sides and three angles. The three sides are straight lines. Triangles are named based on their angles and sides. Equilateral triangles have three equal sides and three 60° angles. Isosceles triangles have two equal sides and two equal angles. Scalene triangles have no equal sides or angles. Right triangles have one 90° angle.
Quadrilaterals
Quadrilaterals are four-sided polygons with four straight sides. The most common types are squares, rectangles, parallelograms, trapezoids, and rhombuses. Squares have four equal sides and four 90° angles. Rectangles have two pairs of equal sides and four 90° angles. Parallelograms have two pairs of parallel sides. Trapezoids have one pair of parallel sides. Rhombuses have four equal sides, but angles are not necessarily 90°.
Regular Polygons
Regular polygons have equal sides and angles. They include triangles, squares, pentagons (5 sides), hexagons (6 sides), octagons (8 sides), decagons (10 sides) and dodecagons (12 sides). As the number of sides increases, the polygon approaches a circle.
Circles
A circle is a set of points in a plane that are the same distance from the center point. Circles are defined by their diameter, which passes through the center and has two endpoints on the circle. The diameter is the longest line that can be drawn in a circle. The radius is the distance from the center to any point on the circle. Circumference is the distance around the circle.
Learning the properties and attributes of basic plane shapes will provide a strong foundation for exploring more complex geometry. Keep practicing identifying different types of triangles, quadrilaterals, regular polygons, and parts of circles. With regular use, you’ll be distinguishing scalene from isosceles triangles and parallelograms from trapezoids in no time!
Examples of Plane Shapes
When it comes to geometry, plane shapes are two-dimensional figures that have length and width, but no depth. Let’s explore some of the most common plane shapes.
- A trapezium is a quadrilateral with two parallel sides. The non-parallel sides are called legs, while the parallel sides are called bases. Trapezoids can have two bases of different lengths.
- A parallelogram also has two pairs of parallel sides, but the sides are of equal length. Squares, rectangles, and rhombuses are all parallelograms.
- A rhombus is a parallelogram with four sides of equal length. The angles of a rhombus can vary, and its sides are parallel to each other. Squares are rhombuses with four 90° angles.
- A square has four sides of equal length and four 90° angles. It is a very common shape used in architecture, designs, and patterns.
- A hexagon is a six-sided polygon with six angles. Regular hexagons have sides of equal length and six angles of 120° each. Hexagons are used in architecture, organic chemistry, and graphic design.
- A circle is a round plane shape where all points are the same distance from the center. Circles are used in wheels, clocks, and many designs. The circumference is the outer perimeter, while a diameter passes through the center.
- A pentagon is any five-sided polygon. A regular pentagon has five sides of equal length and five angles of 108° each. The pentagon shape is commonly found in architecture and graphic design.
- Triangles have three straight sides and three angles that add up to 180°. There are three types: right triangles (one 90° angle), isosceles triangles (two equal sides), and equilateral triangles (three equal sides). Triangles are very stable and are used in construction, design, and engineering.
- Rectangles have two pairs of parallel sides and four 90° angles. The sides of a rectangle are of unequal length. Rectangles are very common shapes used in architecture, signs, doors, windows, rooms, and tables.
Properties and Characteristics of Plane Shapes
Here are some of the properties and characteristics of plane shapes:
- Shape – In geometry, a plane shape refers to a two-dimensional figure that has height and width. Polygon shapes like triangles, squares, rectangles, and circles are common examples of plane shapes.
- Area – The amount of space inside the shape is called the area. Area is measured in square units, such as square inches (in2), square feet (ft2), or square centimeters (cm2). The area formula for each shape is different and depends on its dimensions. For example, the area of a square is side x side, a rectangle is length x width, and a circle is πr2.
- Perimeter – The perimeter refers to the total length of the line segments that form the boundary of the shape. It is measured in linear units, such as inches, feet, or centimeters. The perimeter formula also depends on the shape, such as 4 x side for a square, 2(length + width) for a rectangle, and 2πr for a circle.
- Sides – A side is a straight line segment that forms part of the shape’s outline or boundary. The number of sides determines whether a shape is a triangle (3 sides), square (4 sides), pentagon (5 sides), hexagon (6 sides), and so on. The length of each side depends on the shape and its dimensions.
- Angles – An angle refers to the amount of turn between two straight lines or rays that have a common endpoint. Angles are measured in degrees. The sum of the interior angles of a plane shape depends on the number of sides, such as 180° for a triangle, 360° for a square, and 540° for a pentagon.
- Diagonal – A diagonal is a straight-line segment that joins two non-adjacent vertices of a polygon. Squares, rectangles, and other parallelograms have diagonals that bisect each other. Diagonals are not sides and are not part of the perimeter.
- Axis of Symmetry – An axis of symmetry divides a shape into two congruent halves so that one half can be reflected onto the other. Squares, circles, and regular polygons have multiple axes of symmetry.
What are Open and Closed Shapes?
Open Shapes
Open shapes are those that have gaps or spaces in their outline. They are not enclosed entirely. Some common examples of open shapes are:
- Lines: A line is the simplest open shape. It has two endpoints and extends infinitely in both directions.
- Curves: A curve is a bent or crooked line. It is still an open shape as it is not enclosed.
- Polylines: A polyline consists of multiple line segments joined together. Although it has more than two endpoints, it remains an open shape.
Open shapes are used to represent roads, rivers, trajectories, etc. They imply continuity, direction, and flow.
Closed Shapes
Closed shapes have a defined boundary and their outline encloses an area. Some examples of closed shapes are:
- Circles: A circle is a perfectly round closed shape. It has no corners or edges.
- Ellipses: An ellipse is a closed shape that looks like a squashed circle. It has two focal points within its boundary.
- Squares: A square has four straight sides of equal length and four 90° corners.
- Rectangles: A rectangle also has four straight sides but only two sides of equal length. The other two sides are of different lengths.
- Triangles: A triangle has three straight sides and three corners.
Closed shapes are used to represent enclosed spaces, areas, or objects. They imply containment and occupancy.
Sides and Corners of Shapes
A shape’s sides and corners determine many of its properties and characteristics. The sides refer to the straight lines that enclose the shape, while corners are the points where two sides intersect.
Triangles
Triangles are polygons with three sides and three corners. An equilateral triangle has three equal sides and three 60° corners. An isosceles triangle has two equal sides and two equal corners. A scalene triangle has no equal sides or corners. Triangles are a stable shape because the sides support each other.
Quadrilaterals
Quadrilaterals have four sides and four corners. Squares have four equal sides and four 90° corners. Rectangles have two pairs of equal sides and four 90° corners. Rhombuses have four equal sides with unequal corner angles. Trapezoids have two parallel sides and four corners, with the non-parallel sides of unequal length. Quadrilaterals are a sturdy shape because the four sides anchor each other.
Polygons
Polygons are shapes with three or more straight sides and the same number of corners. Pentagons have five sides, hexagons have six sides, heptagons have seven sides, and so on. As the number of sides increases, the shape becomes closer to a circle. Polygons with more sides tend to be less stable unless all sides and corners are of equal measure.
The number of sides and corners a shape has determines many of its properties, like stability, symmetry, and regularity. Paying attention to these attributes can help in choosing shapes for structural or decorative purposes. Whether building a table or designing a quilt, consider how the sides and corners of each shape will interact with the overall form and function.
What are Straight or Curved Lines?
Lines are one of the most fundamental elements of geometry. They can be either straight or curved.
Straight lines are lines that extend infinitely in opposite directions without bending. They have a constant slope and their path does not deviate. Examples of straight lines are the edges of a ruler or the sides of a square.
Curved lines, on the other hand, bend and change direction gradually. They have varying slopes along their path. Some examples of curved lines are circles, ellipses, parabolas, and hyperbolas. Curved lines are found in nature, architecture, and art. Some common examples you may see every day are the arcs of a bridge, the curves of a race track, or the circular shapes in a floral pattern.
Both straight and curved lines have their place in mathematics and geometry. Straight lines are simpler to define, calculate, and construct while curved lines often appear more organic and natural. Regardless of whether a line is straight or curved, the length of a line is the distance between its endpoints.
Lines have other properties as well, such as:
- Direction: The orientation or slope of a line. Straight lines have a constant direction while curved lines change direction.
- Parallelism: Two lines are parallel if they have the same direction and do not intersect. Railroad tracks are an example of parallel lines.
- Intersection: The meeting point of two lines. Straight lines can intersect at a single point, while curved lines can intersect at multiple points.
- Perpendicularity: Two lines are perpendicular if they intersect at 90 degrees. The letter ‘T’ is made of two perpendicular straight lines.
Lines are fundamental building blocks in geometry, forming the basis for shapes, angles, and more complex figures. Understanding the difference between straight and curved lines is an important first step in geometry.
Solved Examples on Plane Shapes
A plane shape is a two-dimensional flat shape that has a defined boundary. Let’s look at some examples to better understand the different types of plane shapes.
Square
A square has 4 equal sides of the same length and 4 right angles. For example, a square board measuring 5 inches on each side would have an area of 5 x 5 = 25 square inches and a perimeter of 4 x 5 = 20 inches.
Rectangle
A rectangle also has 4 right angles but has 2 pairs of equal sides. For example, a rectangle measuring 10 inches long and 5 inches wide would have an area of 10 x 5 = 50 square inches and a perimeter of 2(10) + 2(5) = 30 inches.
Circle
A circle is a rounded shape where all points are the same distance from the center. For example, a circle with a diameter of 10 inches would have a circumference of π x 10 = 31.4 inches (where π ≈ 3.14) and an area of π x 52 = 78.5 square inches.
Triangle
A triangle has 3 straight sides and 3 angles that add up to 180 degrees. The 3 sides can be of any length. For example, a triangle with side lengths of 6 inches, 8 inches, and 10 inches would have a perimeter of 6 + 8 + 10 = 24 inches. To calculate the area, you would need to know if it is an equilateral, isosceles, or scalene triangle and the measure of the height relative to the base.
In summary, the four basic plane shapes are square, rectangle, circle, and triangle. Each has a distinct shape, number of sides, and formula to calculate perimeter and area. With examples, you can gain a better understanding of these foundational shapes.
What are Examples of Plane Shapes in Everyday Life?
Look around you, plane shapes are everywhere! Here are seven common examples of two-dimensional shapes you encounter in your daily life:
The pages of a book are rectangles. Rectangles are one of the most useful shapes, ideal for maximizing storage space. You’ll find them in book pages, doors, windows, furniture, and buildings.
Your computer or phone screen is a square. Squares are versatile, stable shapes used in architecture, gaming boards, and digital displays. They provide a simple, orderly framework for organizing information.
Coins are circles. Circles represent harmony, continuity, and infinity. They are used for wheels, clocks, plates, and coins which roll and spin.
Road signs are often octagons. Octagons signify stop or caution and are employed for traffic signs, nuts, and bolts. Their eight sides provide stability and strength.
Paper or fabric can be cut into triangles. Triangles are used for sails, kites, tents, and clothing. Their angular shape provides structural support.
Envelopes are diamond-shaped. Diamonds are dramatic, eye-catching shapes used for kites, fabrics, and playing cards. They are often seen as a symbol of value or good luck.
Many paintings or photos use oval shapes. Ovals represent fertility, continuity, and tranquility in art and design. They are used for portraits, mirrors, and decorative accents.
From basic circles to complex polygons, two-dimensional shapes provide useful forms and symbolic meaning in the world around us. Once you start noticing them, you’ll find plane shapes everywhere in your daily life.
How are Plane Shapes Different From Solid Shapes?
Unlike plane shapes, solid shapes have three dimensions, length, width, and depth. They occupy space and volume. Solid shapes, or 3D shapes, include spheres, cubes, pyramids, cylinders, and cones. You can’t draw a solid shape on a piece of paper without it looking flat.
What are Plane Shapes Used For?
Plane shapes are essential in many areas of life. Some of their main uses include:
- Architecture and construction: Shapes like rectangles, triangles, and circles are commonly used.
- Engineering: Many structures are based on simple plane shapes like beams, trusses, and frames.
- Art and design: Plane shapes are fundamental elements of composition, logos, fonts, etc.
- Education: Plane shapes are some of the first geometrical concepts taught to children. They help develop spatial reasoning skills.
- Measurement: Calculating the perimeter, area, diameter, etc. of plane shapes is key to many real-world measurements.
- Packing and tiling: Plane shapes can be used to efficiently pack and tile spaces.
Conclusion
So there you have it, the lowdown on plane shapes. You now know the definition, types, properties, and examples of basic 2D geometrical shapes that are flat and level with straight sides. Whether it’s identifying squares, rectangles, triangles, and circles out in the world or using them in math class, you’ve got this covered. Geometry can actually be pretty fun and fascinating when you take time to notice the plane shapes all around you. And if you ever need a refresher on plane geometry basics, you know where to find this resource.