Geometry
Study of shapes, sizes, properties of space, and geometric relationships.
Basic Concepts
Perimeter, Area, and Volume
Measuring Shapes and Spaces
Geometry helps us measure the world! Three key ideas are perimeter, area, and volume.
Perimeter
Perimeter is the distance around a shape. To find it, add up the lengths of all the sides.
- For a rectangle: \( P = 2(l + w) \)
- For a circle (circumference): \( C = 2\pi r \)
Area
Area is the space inside a shape.
- For a rectangle: \( A = l \times w \)
- For a triangle: \( A = \frac{1}{2}bh \)
- For a circle: \( A = \pi r^2 \)
Volume
Volume measures how much space a 3D object takes up.
- For a cube: \( V = s^3 \)
- For a rectangular prism: \( V = l \times w \times h \)
- For a cylinder: \( V = \pi r^2 h \)
Why Does It Matter?
These measurements help us wrap presents, build houses, or fill a swimming pool!
Key Formula
\[A = l \times w\]
Examples
Finding the area of a garden to buy enough soil.
Measuring the perimeter of a fence for building materials.
In a Nutshell
Perimeter, area, and volume tell us how big shapes and spaces are.