Basic Shapes Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Basic Shapes.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

Closed two-dimensional figures with specific properties like sides, angles, and corners that define their shape.

Shapes are like cookie cutters—circles are round, squares have 4 equal sides.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Shapes are defined by their properties, not their size or orientation.

Common stuck point: Students confuse properties that define a shape (like equal sides for a square) with incidental properties (like orientation). A rotated square is still a square.

Sense of Study hint: Try sorting shapes by counting their sides and corners, then compare which properties stay the same when you rotate or resize them.

Worked Examples

Example 1

easy
How many sides and corners does a rectangle have?

Solution

  1. 1
    Step 1: A rectangle is a closed 2D figure. Count its sides by tracing around it: top, right, bottom, left — that is 4 sides.
  2. 2
    Step 2: Each place where two sides meet is a corner. A rectangle has 4 corners.
  3. 3
    Step 3: Because all corners are right angles (90°), a rectangle is a special type of quadrilateral.

Answer

A rectangle has 4 sides and 4 corners.
Every corner of a rectangle is a right angle. Rectangles belong to the family of quadrilaterals — shapes with exactly four sides.

Example 2

medium
A triangle has 3 sides. A pentagon has 5 sides. How many more sides does a pentagon have than a triangle, and how many corners does each shape have?

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
Which shape has exactly 3 sides: square, triangle, or hexagon?

Example 2

hard
A shape has 6 equal sides and 6 equal corners. What is it called, and what is the sum of all its interior angles?
← Back to Basic Shapes Practice Mode

Background Knowledge

These ideas may be useful before you work through the harder examples.

counting