E5.2 Area and perimeter

Learning objectives

E5.2.1Carry out calculations involving the perimeter and area of a rectangle,• Carry out calculations involving the perimeter and area of a rectangle, triangle, parallelogram and trapezium. Except for the area of a triangle, formulas are not given.

Perimeter is the total distance around a shape; area is the surface enclosed. Choose the calculation from the quantity asked for, not just from the shape's name.

Shape	Area	Perimeter
rectangle, length $l$ , width $w$	$A=lw$	$P=2l+2w$
triangle, base $b$ , perpendicular height $h$	$A=\frac12bh$	add its three side lengths
parallelogram, base $b$ , perpendicular height $h$	$A=bh$	add all sides, or $2(a+b)$
trapezium, parallel sides $a,b$ , perpendicular height $h$	$A=\frac12(a+b)h$	add its four side lengths

Mark the parallel sides and the perpendicular height before substituting. Write the formula, insert values with consistent units, calculate, then attach linear units to perimeter or square units to area. If a dimension is unknown, form the area or perimeter equation first and solve it instead of guessing from the diagram.

A trapezium has parallel sides $7$ cm and $11$ cm and perpendicular height $5$ cm. Its area is $\frac12(7+11)\times5=45\text{ cm}^2$ . If a triangle has area $27\text{ cm}^2$ and base $6$ cm, then $\frac12\times6\times h=27$ , so $h=9$ cm.

A sloping side is not a height unless it is perpendicular to the chosen base. Area alone does not determine perimeter, so every boundary length must be known or derived. Keep compound shapes, circular arcs and sectors for their later Topics.

Next Topic

—E5.3 Circles, arcs and sectorsRead