Geometry: Area of Shapes & Volume of Prisms

Week 8 · Geometry: Area & Volume

Learn to find the area of triangles and parallelograms, and the volume of rectangular prisms.

Area of a Rectangle\nArea = length x width (A = l x w)\n\nA rectangle 8 cm long and 5 cm wide: A = 8 x 5 = 40 sq cm\n\n## Area of a Parallelogram\nA parallelogram is like a slanted rectangle. Use the perpendicular height, not the slant side!\n\nArea = base x height (A = b x h)\n\nParallelogram with base 6 m and height 4 m: A = 6 x 4 = 24 sq m\n\n## Area of a Triangle\nA triangle is half a parallelogram!\n\nArea = 1/2 x base x height (A = 1/2 b h)\n\nTriangle with base 10 ft and height 7 ft: A = 1/2 x 10 x 7 = 35 sq ft\n\n## Volume of a Rectangular Prism\nVolume fills 3D space — measured in cubic units.\n\nVolume = length x width x height (V = l x w x h)\n\nBox 5 cm x 4 cm x 3 cm: V = 5 x 4 x 3 = 60 cu cm

Example 1

📝 Find the area of a triangle with base 12 m and height 5 m.

✓ Answer: 30 sq m

Area = 1/2 x base x height = 1/2 x 12 x 5 = 6 x 5 = 30 sq m.

Example 2

📝 A rectangular box is 6 cm long, 4 cm wide, and 3 cm tall. What is its volume?

✓ Answer: 72 cu cm

Volume = l x w x h = 6 x 4 x 3 = 72 cu cm.

⚠️Using the slant side instead of the perpendicular height for parallelograms and triangles
⚠️Forgetting the 1/2 in the triangle area formula
⚠️Mixing up area (flat, square units) and volume (3D, cubic units)