Mensuration: notes

Area and Perimeter

• Rectangle: area = length x width. Perimeter = 2(l + w).
• Triangle: area = 1/2 x base x height. The height is at right angles to the base.
• Parallelogram: area = base x height.
• Trapezium: area = 1/2 (a + b) h, where a and b are the parallel sides.
• Circle: circumference = 2 pi r, area = pi r^2. Use pi = 3.14 or 22/7 as the question says.

Arcs and Sectors

• Arc length = (angle / 360) x 2 pi r.
• Sector area = (angle / 360) x pi r^2.

Solids

• Prism volume: area of cross-section x length.
• Cylinder: volume = pi r^2 h. Curved surface area = 2 pi r h.
• Cone: volume = 1/3 pi r^2 h. Pyramid: volume = 1/3 x base area x height.
• Sphere: volume = 4/3 pi r^3. Surface area = 4 pi r^2.

Units

• Area units: 1 m^2 = 10 000 cm^2, because 100 x 100.
• Volume units: 1 m^3 = 1 000 000 cm^3. 1 litre = 1000 cm^3.
• Scale factor k: lengths scale by k, areas by k^2, volumes by k^3.