What Is a Plane Shape?
A plane shape is a flat, two-dimensional figure that lies entirely on a single flat surface. It has length and width, but no thickness or depth. Because it is flat, a plane shape is also called a two-dimensional shape or a plane figure.
Two simple ideas describe a plane shape:
It is flat. The whole shape sits on one flat surface, like a drawing on a sheet of paper.
It has two dimensions. You can measure how long and how wide it is, but not how thick, because it has no thickness.
Plane shapes are different from solid (3D) shapes such as cubes and spheres, which also have depth. A drawing of a circle is a plane shape; a ball is a solid shape. Plane shapes are the simplest members of the wider family of shapes in geometry.
Why Can You Draw a Square but Never Hold a Flat One?
Draw a square on paper and it looks solid, but a true square has no thickness at all.
That is the strange, useful idea behind a plane shape: it lives on a flat surface, with only length and width, and zero depth. You can picture it, sketch it, and measure it, but you can never pick a perfectly flat shape up, because it has nothing to grip. These flat figures, the 2D shapes you meet first in geometry, are the building blocks of almost every drawing, sign, and screen around you.
What Are the Types of Plane Shapes?
Plane shapes are sorted by how many straight sides they have, or whether they are curved.
Shape | Number of sides | Note |
|---|---|---|
Triangle | 3 straight sides | The polygon with the fewest sides |
Square | 4 equal straight sides | All angles are right angles |
Rectangle | 4 straight sides | Opposite sides equal, all right angles |
Pentagon | 5 straight sides | A five-sided polygon |
Hexagon | 6 straight sides | A six-sided polygon |
Circle | No straight sides | A curved shape, not a polygon |
Oval (ellipse) | No straight sides | A stretched, curved shape |
Shapes made only of straight sides that join up are called polygons. A circle is a plane shape too, but it is not a polygon because it is made from a curved line, not straight sides.
What Are the Properties of Plane Shapes?
Every plane shape can be described using a few simple features.
Sides. The straight lines that make up a shape are its sides. A triangle has 3 sides; a square has 4.
Corners (vertices). The points where two sides meet are corners, also called vertices. A triangle has 3 corners.
Curved or straight. Some plane shapes are made of straight sides (square, triangle), and some are made of curved lines (circle, oval).
Open or closed. A shape that starts and ends at the same point is closed; a shape with a gap is open.
Flat. Every plane shape is flat, with length and width only.
What Is the Difference Between Open and Closed Plane Shapes?
Plane shapes can be open or closed, and this depends on whether the shape joins back to where it started.
A closed shape begins and ends at the same point, with no gaps. Triangles, squares, and circles are closed. Read more about these in closed shapes.
An open shape does not end at its starting point, so it has a gap. A single line segment, a curve that does not join up, or the letter "C" shape are open.
Only closed plane shapes can have an inside and an outside, which is why we can find the area of a closed shape but not of an open one.
Where Are Plane Shapes Used?
Plane shapes appear all around us, once you start looking.
Signs and symbols. A stop sign is a plane hexagon (an octagon, in fact), a yield sign is a triangle, and many warning signs are plane shapes chosen so they are easy to recognise.
Buildings and design. Windows, doors, tiles, and floor plans are drawn as plane shapes before anything is built.
Screens and art. Every picture on a screen is built from tiny plane shapes, and artists sketch with circles, squares, and triangles first.
Everyday objects. The face of a clock is a circle, a chessboard is made of squares, and a slice of pizza is close to a triangle.
Examples of Plane Shapes
Example 1
How many sides and corners does a rectangle have?
A rectangle is a plane shape with four straight sides. Where two sides meet is a corner.
A rectangle has 4 sides and 4 corners.
Final answer: 4 sides and 4 corners.
Example 2
Is a circle a polygon?
Wrong path. A student says "a circle is a closed plane shape, and polygons are closed plane shapes, so a circle must be a polygon."
Why it breaks. Being closed is not enough. A polygon must be made only of straight sides that join up. A circle is made from a single curved line, so it has no straight sides at all.
The rescue. Check for straight sides first. A circle is a closed plane shape, but because it is curved, it is not a polygon.
Final answer: no, a circle is not a polygon because it has no straight sides.
Example 3
Sort these into open or closed: (a) a triangle, (b) the letter "U", (c) a square.
A shape is closed if it starts and ends at the same point with no gap.
(a) A triangle joins back to its start, so it is closed.
(b) The letter "U" has a gap at the top, so it is open.
(c) A square joins back to its start, so it is closed.
Final answer: triangle: closed; "U": open; square: closed.
Example 4
Which plane shape has 3 straight sides and 3 corners?
A shape with exactly 3 straight sides that join up is a triangle.
Final answer: a triangle.
Example 5
A plane shape has 6 equal straight sides. Name it.
A polygon with 6 straight sides is a hexagon. When all six sides are equal, it is a regular hexagon.
Final answer: a hexagon.
Example 6
Find the area of a square-shaped tile whose side is $5$ cm.
The area of a square is side $\times$ side.
$$\text{Area} = 5 \times 5 = 25 \text{ cm}^2$$
Final answer: the area is $25$ square centimetres.
Where Do Students Trip Up on Plane Shapes?
The most common mix-up is between plane (flat) shapes and solid shapes. Students first learning shapes often call a ball a "circle" or a box a "square," when a ball is a solid sphere and a box is a solid cube. Asking "can I hold it, or is it just flat?" separates the two: if it has thickness, it is a solid shape, not a plane shape.
Mistake 1: Confusing plane shapes with solid shapes
Where it slips in: Naming everyday objects like balls, dice, and cans.
Don't do this: Calling a ball a circle or a dice a square.
The correct way: A circle and a square are flat plane shapes. A ball is a solid sphere and a dice is a solid cube. Flat means plane; thick means solid.
Mistake 2: Thinking every closed shape is a polygon
Where it slips in: Sorting circles and ovals with polygons.
Don't do this: Putting a circle in the polygon group just because it is closed.
The correct way: A polygon must have only straight sides. Circles and ovals are closed plane shapes, but they are curved, so they are not polygons.
Mistake 3: Miscounting sides and corners
Where it slips in: Naming shapes with more sides, like pentagons and hexagons.
Don't do this: Guessing the name without counting.
The correct way: Count the straight sides one by one, then name the shape. Miscounting matters in the real world too: honeycomb cells are built as hexagons because six-sided shapes tile together with no gaps, and getting the side count wrong would break the whole pattern.
Conclusion
Plane shapes are flat, two-dimensional figures with length and width but no thickness.
Their main types are the triangle, square, rectangle, pentagon, hexagon, circle, and oval.
Shapes with only straight sides that join up are polygons; a circle is a plane shape but not a polygon.
Plane shapes are described by their sides, corners, and whether they are open or closed, curved or straight.
Plane shapes differ from solid (3D) shapes, which also have depth.
To take plane shapes further with a teacher, explore Bhanzu's geometry tutor or elementary math tutor sessions, or browse math classes for kids for hands-on shape practice.
Read More
Practice These to Solidify Your Understanding
Work through these problems in order:
How many sides and corners does a pentagon have?
Is an oval a polygon? Explain in one sentence.
Sort these into open or closed: a full circle, the letter "C", a square.
Answer to Question 1: 5 sides and 5 corners. Answer to Question 2: No, an oval is not a polygon because it is curved and has no straight sides. Answer to Question 3: Full circle: closed; letter "C": open; square: closed.
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