Area, Volume & Circles

Area of 2D shapes, volume of prisms, surface area and circle formulae – high-frequency exam topics.

You must know the standard area and volume formulae and apply them in exam problems, including compound shapes.

Key area formulae

• Rectangle: length × width • Triangle: ½ × base × height • Parallelogram: base × perpendicular height • Trapezium: ½(a + b) × height • Circle: πr² • Circumference: 2πr or πd

Worked example

A triangle has base 12 cm and height 7 cm. Find its area.

Solution

Area = ½ × 12 × 7 = **42 cm²**

Volume of a prism

Volume of any prism = area of cross-section × length Cylinder is a circular prism: Volume = πr²h

Worked example

A cylinder has radius 4 cm and height 10 cm. Find its volume in terms of π.

Solution

V = π × 4² × 10 = π × 16 × 10 = **160π cm³**

Surface area of a cuboid / cylinder

Cuboid: 2(lw + lh + wh) Cylinder: 2πr² + 2πrh (two circles + curved rectangle)

Worked example

A cuboid measures 5 cm × 3 cm × 2 cm. Find its surface area.

Solution

2(5×3 + 5×2 + 3×2) = 2(15 + 10 + 6) = 2 × 31 = **62 cm²**

Practice questions

Try these without looking at the answers first.

Q1.Area of a trapezium with parallel sides 8 cm and 12 cm, height 5 cm?

Show answer

50 cm²

Q2.Volume of a cuboid 6 cm × 4 cm × 3 cm?

Show answer

72 cm³

Q3.Circumference of a circle radius 7 cm (use π = 22/7)?

Show answer

44 cm

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