Time is used to measure periods such as the numbers of weeks until a birthday, the number of days until the holidays, or the number of minutes left in a maths lesson.

The metre is the standard unit of length in the metric system.

(a) When converting to a larger unit, divide.

(b) When converting to a smaller unit, multiply.

1 cm = 10 mm1 m = 100 cm1 km = 1000 m

The perimeter of a shape is the total distance around that shape.

For circular figures the term circumference is used instead of perimeter.

A formula can be used to find the perimeter (or circumference) of each of the following shapes.

(a) Square

P = 4l

(l = side length)

(b) Rectangle

P = 2(l + w)

(l = length, w = width)

(c) Circle

C = 2πr

(r = radius) or

C = πd

(d = diameter)

When finding the perimeter of a shape, make sure that all measurements have the same units.

Area

The area of a shape is a measure of the amount of surface enclosed by that shape.

Area is measured in units based on the square metre, such as the square centimetre (cm2). The conversion between square units is the square of the conversion between linear units.

A formula can be used to calculate the area of simple shapes.

(a) Square

A = l2

(l = length)

(b) Rectangle

A = lw

(l = length, w = width)

(c) Triangle

A = 0.5bh

(b = base, h = height)

(d) Circle

A = πr2

(r = radius)

(e) Parallelogram

A = bh

(b = base, h = height)

(f) Trapezium

A = 0.5(a + b)h

(a, b = parallel sides, h = height)

The area of a composite shape can be found by dividing the shape into simpler shapes and using the appropriate formula.

Area and perimeter of a sector

A sector is a portion of a circle formed by two radii and the arc between them.

To find the area of a sector, use the formula A = θ/360 πr2, where θ is the angle included between the radii.

To find the perimeter of a sector, use the formula l = θ/360 × 2πr, where θ is the angle included between the radii, to find the curved side. Then add the lengths of all sides to find the total perimeter.

Surface area of rectangular and triangular prisms

Prisms are 3-dimensional figures, which have uniform cross-sections (that are polygons).

The surface area of a prism is the area of its outside surface.

To find the surface area of a prism, find the area of each face using the correct area formula, and add them together. Consider the front, back, left, right, top and bottom sides.

Look for identical faces, which will have the same area.

The surface area (SA) of a rectangular prism (or a cuboid) of length l, width w and height h is given by the formula SA = 2(lh + lw + wh).

419Surface area of a cylinder

The outer surface of a cylinder is made up of two circles and a rectangle.

The area of the rectangular curved surface is given by the formula A = 2πrh.

To find the surface area of a cylinder, use the formula SA = 2πrh + 2πr2, where r is the radius of the base and h is the height of the cylinder.

The formula can be simplified to SA = 2πr(r + h).

Volume of prisms (including cylinders)

The volume of a solid is the amount of space it occupies.

Volume is measured in cubic units, such as cubic millimetres (mm3), cubic centimetres (cm3) and cubic metres (m3).

The volume of any prism can be found by multiplying the area of its cross-section (or base), A, by its height, h; that is, V = Ah.

The volume of a cylinder is given by the formula V = πr2h.

Capacity is a term usually applied to the measurement of liquids.

The…