Measuring Space: Flat and 3D Shapes

Geometry is about shapes and the space they take up. Area measures how much flat space a shape covers. Surface area is the total area of all surfaces on a 3D object. Volume is the space inside a 3D object.

Area

• Rectangle: \( \text{Area} = \text{length} \times \text{width} \)
• Triangle: \( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \)

Surface Area

Add up the area of every face of the solid. For a rectangular prism, add the areas of all six sides.

Volume

• Rectangular prism: \( \text{Volume} = \text{length} \times \text{width} \times \text{height} \)

Real-World Uses

• Finding how much paint you need for a wall (area).
• Wrapping a present (surface area).
• Filling a fish tank with water (volume).