Area and Perimeter Basics
Area and Perimeter
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Area and Perimeter
Open the lesson by framing area and perimeter as two different measures that students often mix up: distance around a shape and space inside a shape.
Today’s goal
I can work out area and perimeter, including compound shapes, missing lengths and exam-style questions.
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What words come to mind when you hear area and perimeter?
Use this to surface prior knowledge and misconceptions, especially confusion between inside space, outside distance and units.
Quick diagnostic check
Short mixed questions
Number
Fractions, decimals and percentages
Ratio and algebra
Angles, graphs and probability
Area and perimeter
This slide anchors the purpose of the opening assessment without turning it into an activity slide. Use results to spot whether errors come from recall, method, or reading exam questions.
What the check tells us
A wrong answer does not always mean the same problem.
Forgotten knowledge: a fact or formula is missing
Misunderstanding: the method is mixed up
Exam technique: the maths is known, but the question is read badly or steps are skipped
Keep this short. It sets up why the lesson now focuses on area and perimeter: students have already identified this as a weak area, so the main teaching time goes there.
Perimeter and area are different
Perimeter = distance around the outside
Area = space inside the shape
Perimeter uses units like cm
Area uses square units like cm²
This distinction is the key misconception to fix early. Stress that area and perimeter can change differently even in shapes that look similar.
Perimeter of rectangles
Add all the side lengths
In a rectangle, opposite sides are equal
This gives perimeter = 2 × length + 2 × width
Example: length 8 cm, width 3 cm
Perimeter = 8 + 3 + 8 + 3 = 22 cm
You can also show the shortcut 2(length + width), but keep the wording consistent with adding all sides first.
Perimeter of compound shapes
Trace the outside edge only
Include every outer side once
Do not count inner lines
Find any missing side lengths before adding
Students often add all visible lines, including interior splits. Emphasise the phrase outside edge only.
Finding missing lengths
Missing lengths in rectilinear shapes come from equal horizontal or vertical totals.
Match widths with widths
Match heights with heights
Use subtraction to find the unknown side
Then use the full set of outer lengths for perimeter or split the shape for area
A useful teacher model is to mark parallel horizontal sides in one colour and vertical sides in another, so equal totals stand out.
Which measure means distance around a shape?
Area
Perimeter
Height
Square units
Checks the key distinction from slides 4–7. Distractors target common vocabulary mix-ups.
Perimeter and missing lengths
To find the perimeter of a compound shape, trace the outside edge only. In a rectangle, opposite sides are equal. If a side is missing, use subtraction before adding the outer lengths.
Echoes the wording from slides 5–7 so students rehearse the method, not just isolated words.
Area of rectangles
Area = length × width
Multiply the two side lengths
Write the answer in square units
Example: 9 cm × 4 cm = 36 cm²
Link this to counting unit squares if needed. This helps students see why the formula works, rather than treating it as a rule to memorise only.
Area of triangles
Area = 1/2 × base × height
The height must be perpendicular to the base
A triangle has half the area of a matching rectangle or parallelogram
Students may use a sloping side instead of the perpendicular height. Point clearly to the right angle in the height line.
Area of parallelograms
Area = base × perpendicular height
Do not use the sloping side as the height
A parallelogram can be rearranged into a rectangle with the same area
This is another common confusion point: students often multiply base by slanted side. Keep the term perpendicular height consistent with the triangle slide.
Area of compound shapes
For a compound shape, split it into simple shapes.
Use rectangles, triangles or parallelograms
Work out each area separately
Add the parts together
Keep the same units all the way through
If students struggle, draw faint split lines to show possible decompositions. There may be more than one correct way to split the same shape.
For a triangle, which height should you use?
The longest side
The sloping side
Any vertical side
The perpendicular height
Checks the misconception highlighted on the triangle and parallelogram slides.
Area rules
The area of a rectangle is length × width. The area of a triangle is 1/2 × base × height. For a compound shape, split it into simple shapes and add the parts.
All blanks are load-bearing ideas from slides 8–11.
How would you find the area of a compound shape?
Expected elements: split the shape into simple parts, use the correct area formula for each part, then add the areas. Accept brief method descriptions in students’ own words.
Units and conversions
Perimeter uses single units: mm, cm, m
Area uses square units: mm², cm², m²
Convert lengths before using a formula
Mixed units can lead to a wrong answer
Keep conversions simple and practical for Foundation: for example, convert all lengths to cm before finding area or perimeter.
Reading word problems
Decide first: is the question asking for perimeter or area?
Underline the given lengths and units
Sketch the shape if needed
Find missing lengths before calculating
Check whether the answer should be in units or square units
This slide addresses exam technique directly. Students often know the maths but choose the wrong measure because of the wording.
Exam-style method
Strong exam answers usually show each step clearly.
Write the formula or method
Show any missing length working
Calculate carefully
Include the correct units
Check if the answer is sensible
For 4–5 mark questions, method marks matter. Encourage students to lay out working so that a marker can follow each step.
Longer exam questions
Multi-step questions may mix missing lengths, area and perimeter
Break the shape into parts
Solve one step at a time
Keep earlier answers to use in later steps
This prepares students for the one- or two-question finish mentioned in the brief, without turning the slide into an activity.
Key ideas to remember
Perimeter is around the outside
Area is inside the shape
Use the correct formula
Find missing lengths first
Check units at the end
Use this as a bridge into final exam-style practice or teacher modelling.
What should you do before using a formula with mixed units?
Round the lengths
Convert the lengths
Add the units
Square the lengths
Checks slide 12 directly and prepares for word problems.
Exam-style steps
In a word problem, decide first if the question wants perimeter or area. Show any missing length working and check the final units at the end.
Reinforces exam technique from slides 13–16.
What part of area and perimeter feels hardest now?
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What is one thing you will remember from this lesson?
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Glossary
perimeter - the total distance around the outside of a shape
area - the amount of space inside a shape
compound shape - a shape made from two or more simple shapes
rectangle - a four-sided shape with four right angles
triangle - a three-sided shape
parallelogram - a four-sided shape with opposite sides parallel
units - the measures used in an answer, such as cm or m²
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Glossary
square units - units used for area, such as cm² or m²
base - the chosen bottom side used in an area formula
height - the perpendicular distance from the base
perpendicular - meeting at a right angle
convert - change a measurement into another unit
exam-style question - a question that needs clear working as well as the final answer
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