Plane vs. Solid Geometry

Contributor: Ashley Nail. Lesson ID: 13235

Learn the difference between plane and solid geometry. Practice sorting different types of 2D and 3D shapes before crafting your very own solid-shape garland!

categories

Geometry, Measurement and Data

subject
Math
learning style
Kinesthetic, Visual
personality style
Lion, Beaver
Grade Level
Intermediate (3-5), Middle School (6-8)
Lesson Type
Quick Query

Lesson Plan - Get It!

Audio:

Before we learn about plane and solid geometry, let's draw a picture!

Grab a piece of scrap paper and a pencil, and draw the following:

  • a kid playing with a ball
  • a kid holding an ice cream cone
  • a house with a pointy roof
  • a cat standing on a box

Now, you don't have to be an amazing artist, but I bet you drew a picture similar to mine.

shape drawing

Look at your drawing. Find the ball.

  • What shape did you draw for the ball?

A circle!

Find any triangles, squares, or rectangles you drew on your picture!

You may not know it, but your drawing proves you already know a lot about plane and solid geometry!

Plane vs. Solid Geometry

A ball, an ice cream cone, a house, and a box are all three-dimensional, or 3D, shapes. For example, a ball is round. You can hold it and turn it and touch all around the surface of the ball. But when you draw it, you draw a circle. The circle you drew on your paper is flat.

Same thing with the box. When you hold a box, it has six sides. The 3D box can be filled on the inside. However, when you drew the box, you drew a flat rectangle or square with four sides.

The circle, rectangle, square, and triangle are all examples of plane geometry. These shapes exist in two dimensions (2D).

When you draw a rectangle, for example, it has two measurements: length and width.

rectangle

These two measurements represent the two-dimensional plane that this shape exists in. A two-dimensional plane is a flat surface, like an endless piece of paper.

Solid shapes, like a box, are different from plane shapes because they have a third dimension.

  • Remember the rectangle?

It had two dimensions: length and width. When you drew your picture earlier, the paper you drew on was on a flat surface, like a desk or a table.

flat surface rectangle

Now, a solid shape adds another dimension. This measurement is the height.

solid rectangle

Solid shapes are 3D and have length, height, and width.

Types of Plane Shapes

There are two types of plane shapes: polygons and round shapes.

Polygons are two-dimensional plane shapes that are made of straight lines that connect.

For example, a square and rectangle are polygons.

  • Can you think of any more?

polygons

Triangles, pentagons, trapezoids, parallelograms, hexagons, octagons, rhombus are all examples of polygons and plane shapes.

Round shapes are plane shapes that are two-dimensional and have continuous rounded lines.

round shapes

Types of Solid Shapes

There are two types of solid shapes: polyhedra and non-polyhedra.

Polyhedras are three-dimensional solid shapes that have flat surfaces. Cubes, pyramids, and prisms are examples of polyhedra solid shapes.

polyhedra shapes

Non-polyhedras are three-dimensional shapes where a surface is not flat, but rounded. Spheres, cones, and cylinders are all examples of these solid shapes.

non-polyhedra shapes

Now that you know the difference between plane and solid geometry as well as the types of plane and solid shapes, visit the Got It? section to practice identifying these shapes.

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