Shapes tell us about space.
Geometry gives us a mathematical language for describing objects and spaces. A shape can have edges, vertices, angles, curved boundaries, or a combination of these features.
Start with a few familiar two-dimensional shapes.
Square
Four equal sides and four right angles.
Rectangle
Opposite sides are equal and all angles are right angles.
Triangle
Three sides. Its interior angles add up to 180°.
Circle
A curved boundary whose points are equally distant from its centre.
Perimeter is not area.
Two measurements are especially useful. Perimeter measures the distance around a two-dimensional shape. Area measures the amount of surface enclosed by its boundary.
The rectangle has length 4 units and width 3 units.
l = 4, w = 3Add all four sides, or double the sum of length and width.
P = 2(4 + 3) = 14Multiply the length by the width.
A = 4 × 3 = 12The rectangle's perimeter is 14 units, while its area is 12 square units. Notice that perimeter and area use different kinds of units: ordinary units for length and square units for area.
Change a shape. Discover what changes.
Choose a rectangle, circle, or right triangle. Adjust the dimensions and compare the area with the perimeter. The diagram and calculations update as you experiment.
Interactive shape explorer
Enter positive dimensions. The diagram is illustrative; the displayed calculations use your exact values.
Area = length × width. Perimeter = 2 × (length + width).
Solve these geometry questions.
Read each question carefully. Pay attention to whether it asks for a perimeter, area, or angle.
A rectangle is 6 units long and 3 units wide. What is its area?
Enter the numerical answer.
From flat shapes to deeper ideas.
Geometry begins with simple shapes but extends to coordinate systems, transformations, proofs, and three-dimensional objects. Once you understand how dimensions affect area and perimeter, you are ready to explore more complex relationships.