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!