Plane Figure
Plane Figure
A shape on a plane. Includes points, lines, polygons,
polygon interiors, circles, disks, parabolas, ellipses, hyperbolas,
etc. Formally, a plane figure is any set of points on a plane.
See also
Worked Example
Problem: A rectangle has a length of 8 cm and a width of 5 cm. Confirm that this is a plane figure and find its area and perimeter.
Step 1: Identify the shape. A rectangle is a polygon with four sides and four right angles. It lies flat on a single plane, so it is a plane figure.
Step 2: Since this is a two-dimensional plane figure, you can calculate its area using length times width.
A=l×w=8×5=40 cm2
Step 3: You can also calculate its perimeter, which is the total distance around the figure.
P=2(l+w)=2(8+5)=26 cm
Answer: The rectangle is a plane figure with an area of 40 cm² and a perimeter of 26 cm.
Another Example
Problem: Which of the following are plane figures: a triangle, a sphere, a circle, a cube, and a line segment?
Step 1: A plane figure must lie entirely in one flat plane and be two-dimensional. Check each shape against this requirement.
Step 2: A triangle is a polygon with three sides — it lies flat on a plane. It is a plane figure.
Step 3: A sphere is a three-dimensional object (it has depth). It is NOT a plane figure.
Step 4: A circle is a set of points equidistant from a center, all lying on a single plane. It is a plane figure.
Step 5: A cube is a three-dimensional solid with six square faces. It is NOT a plane figure.
Step 6: A line segment connects two points on a plane. It is a plane figure.
Answer: The triangle, circle, and line segment are plane figures. The sphere and cube are not, because they are three-dimensional.
Frequently Asked Questions
What is the difference between a plane figure and a solid figure?
A plane figure is flat and two-dimensional — it has only length and width (like a square or circle). A solid figure is three-dimensional — it has length, width, and height or depth (like a cube or sphere). You can draw a plane figure on a sheet of paper, but a solid figure occupies volume in space.
Is a circle a plane figure?
Yes. A circle is a set of points on a plane that are all the same distance from a central point. Because every point of a circle lies on a single flat surface, it qualifies as a plane figure.
Plane Figure vs. Solid Figure
A plane figure exists entirely on one flat surface and has two dimensions (length and width). Examples include triangles, circles, and rectangles. A solid figure extends into three dimensions (length, width, and depth) and occupies volume. Examples include cubes, spheres, and cylinders. Every face of a solid figure is itself a plane figure, but the solid as a whole is not.
Why It Matters
Plane figures form the foundation of two-dimensional geometry. When you calculate area, perimeter, or work with coordinate graphs, you are working with plane figures. Understanding them is also essential for studying three-dimensional shapes, since every solid is bounded by flat or curved surfaces that relate back to plane figures.
Common Mistakes
Mistake: Confusing a plane figure with a solid figure, such as calling a cube a plane figure.
Correction: A plane figure must be entirely flat and two-dimensional. A cube has depth and volume, making it a solid (three-dimensional) figure. Only its individual faces — which are squares — are plane figures.
Mistake: Thinking plane figures must be closed shapes like polygons or circles.
Correction: Points, lines, line segments, rays, and open curves are also plane figures, because they are sets of points lying on a plane. A plane figure does not have to enclose an area.
Related Terms
- Plane — The flat surface on which plane figures exist
- Polygon — A closed plane figure with straight sides
- Circle — A curved plane figure with constant radius
- Geometric Figure — Broader category including plane and solid figures
- Disk — A circle together with its interior region
- Point — The simplest possible plane figure
- Line — An infinite straight plane figure
- Ellipse — An oval-shaped plane figure (conic section)