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.

Practice lesson for the WJEC Mathematics and Numeracy Double Award. This is not an official WJEC page.

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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