Perimeter and composite area | Year 11

01 / LEARN

Understand the idea.

Understand the idea

Perimeter measures the distance around the outside edge; area measures the region enclosed. A line drawn to split a shape helps calculate area but is not another edge to fence. Trace the actual boundary before choosing a perimeter calculation.

For composite area, split the region into non-overlapping familiar shapes, or subtract a missing part from a larger enclosing shape. Label which region each calculation measures so parts are neither omitted nor counted twice.

Choose and apply a method

Convert all lengths to a common unit first. Rectangle area uses length times width; triangle area uses half the base times its perpendicular height. A sloping side cannot replace the height unless it is perpendicular to the chosen base.

Translate the context after calculating: an entrance reduces fencing, while a removed corner reduces floor area. Keep length units for boundary distances and square units for areas. Check that a region with a part removed is smaller than its enclosing rectangle.

\begin{aligned} A_{rectangle} & = l w \\ A_{triangle} & = \frac{1}{2} b h \end{aligned}

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Remove a corner

A 12 m by 6 m rectangle has a 4 m by 3 m corner removed. Find remaining area.

Worked solution

1
Find the enclosing rectangle's area.
$A_{whole} = 12 \times 6 = 72 m^{2}$
The remaining region and the missing corner together form this rectangle.
2
Find the removed corner's area.
$A_{corner} = 4 \times 3 = 12 m^{2}$
The removed part is a rectangle with the stated dimensions.
3
Subtract the missing area.
$A = 72 - 12 = 60 m^{2}$
Only the area still present belongs to the L-shaped region.

Answer

60 m $2$ .

EXAMPLE 02

Leave an entrance

A garden is 8 m long and 5 m wide. A 2 m entrance is left unfenced. Find required fencing.

Worked solution

1
Find the full rectangular boundary.
$P = 2 (8 + 5) = 26 m$
A rectangle has two lengths and two widths.
2
Remove the unfenced entrance.
$F = 26 - 2 = 24 m$
The entrance is part of the perimeter but does not require fencing.
3
Interpret the result.
$F = 24 m$
Fencing is a boundary length, so the result uses metres rather than square metres.

Answer

24 m.

03 / YOUR TURN

Try it yourself.

Check your understanding

A 10 cm by 7 cm rectangle has a 3 cm by 2 cm corner removed. Find area.

Show answer & reasoning

64 cm $2$ .

Calculate the full rectangle and subtract the missing corner: $A = 10 \times 7 - 3 \times 2 = 70 - 6 = 64 {cm}^{2}$ . Both products measure areas in the same square unit.

Keep practising

6 worksheet questions · 13 marks

Open worksheet Worked solutions

Read the questions online

Find perimeter and area of a 9 m by 4 m rectangle.
2 marks
A 15 m by 8 m rectangle has a 5 m by 3 m corner removed. Find area.
2 marks
A triangle has base 14 cm and perpendicular height 9 cm. Find area.
2 marks
Find perimeter of the illustrated L-shape.
3 marks
A 6 m by 4 m room has a 2 m by 1 m alcove added outside a wall, with no overlap. Find floor area.
2 marks
A circular pond has radius 3 m. Find circumference to 2 decimal places.
2 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Find perimeter and area of a 9 m by 4 m rectangle.
2 marks
$P = 2 (9 + 4) = 26$ .
$A = 9 \times 4 = 36$ .
26 m; 36 m $2$ .
A 15 m by 8 m rectangle has a 5 m by 3 m corner removed. Find area.
2 marks
$15 \times 8 - 5 \times 3 = 120 - 15 = 105$ .
105 m $2$ .
A triangle has base 14 cm and perpendicular height 9 cm. Find area.
2 marks
$A = \frac{1}{2} \times 14 \times 9 = 63$ .
63 cm $2$ .
Find perimeter of the illustrated L-shape.
3 marks
The removed outer lengths are replaced by equally long notch edges.
Perimeter remains $2 (12 + 6) = 36$ m.
36 m.
A 6 m by 4 m room has a 2 m by 1 m alcove added outside a wall, with no overlap. Find floor area.
2 marks
$6 \times 4 + 2 \times 1 = 24 + 2 = 26$ .
26 m $2$ .
A circular pond has radius 3 m. Find circumference to 2 decimal places.
2 marks
$C = 2 π r = 6 π$ .
$6 π \approx 18.85$ m.
18.85 m.

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Curriculum reference & lesson scope

SACE Board of South Australia

Stage 1 General Mathematics measurement skills and applications; original explanatory lessons and papers.

Official curriculum source ↗

In this lesson

Understand the idea.

Understand the idea

Choose and apply a method

See the method in action.

Remove a corner

Find the enclosing rectangle's area.

Find the removed corner's area.

Subtract the missing area.

Leave an entrance

Find the full rectangular boundary.

Remove the unfenced entrance.

Interpret the result.

Try it yourself.

Check your understanding

Keep practising