Areas of Rectangles and Triangles
Finding Area Step by Step
Lesduur is: 120 minOnderdelen in deze les
Finding Area Step by Step
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Learning goal
I can work out the area of a rectangle, a compound shape and a triangle using the correct formula and units.
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One word or phrase you link with area
Use this to surface prior ideas such as space inside, length × width, squares, units, rectangle, triangle, or perimeter as a misconception to address.
Area of a rectangle
Area measures the space inside a shape
For rectangles, use length × width
Area is written in square units
Examples: cm², m², mm²
Stress that area is two-dimensional space, not distance around the edge. Students often confuse area with perimeter.
Before multiplying
Check the length and width use the same unit
If not, convert one so they match
Then multiply the two measurements
A quick example to mention aloud: 2 m and 50 cm must be converted before multiplying.
Writing the answer
Multiply length × width
Write the answer with the correct square unit
If the measurements are in millimetres, the area is in mm²
If the measurements are in metres, the area is in m²
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Rectangle example
The length and width are both measured in millimetres.
18 × 5 = 90
The area of the rectangle is 90 mm².
Emphasise why the unit becomes mm²: one dimension is in mm and the other is in mm, so the area is square millimetres.
Finding a missing side
If you know the area and one side, divide
length = area ÷ width
width = area ÷ length
Write the answer in a unit of length, not a square unit
Point out the inverse relationship: multiplication finds area, division finds a missing side.
What must you check before finding a rectangle's area?
Same units
Same shape
Same area
Same perimeter
Tests the key step from the rectangle method: measurements must match before multiplying.
Rectangle area and missing side
To find the area of a rectangle, multiply the length by the width. Write the answer in square units. If one side is missing, divide the area by the known side.
The blanks target the core process and the inverse idea: multiply for area, divide for a missing side.
Compound shapes
A compound shape is made from simpler shapes joined together
Many compound shapes can be split into rectangles
Their area can be found in more than one way
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Method 1: add rectangles
Split the shape into rectangles
Find each rectangle's area
Add the areas to get the total
Make clear that students should only split the shape into parts with known or findable lengths and widths.
Addition method
Rectangle 1 area = length × width
Rectangle 2 area = length × width
Total area = area of rectangle 1 + area of rectangle 2
You can generalise aloud that this works for three or more rectangles as well.
Method 2: subtract a cut-out
See the shape as one large rectangle
Identify the missing small rectangle
Find both areas
Subtract the cut-out area
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Subtraction method
Area of compound shape = area of large rectangle - area of cut-out rectangle
Sometimes this is quicker than splitting the shape into several smaller rectangles.
Highlight that both methods should give the same answer when used correctly.
Which method uses a large rectangle and a cut-out?
Triangle method
Subtraction method
Division method
Addition method
Checks whether students can distinguish the two compound shape methods.
Two ways to find compound area
A compound shape can be split into rectangles and the parts can be added. Another way is to find a large rectangle and subtract the area of the cut-out.
Echoes the lesson wording so students secure both addition and subtraction approaches.
Area of a triangle
The area of a triangle is:
A = ½ × b × h
b is the base
h is the perpendicular height
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Why there is a half
A rectangle can be divided into two congruent triangles
Each triangle is half the area of the rectangle
So triangle area is ½ × base × height
Link this back to rectangle area so students see the triangle formula as a generalisation, not a new rule to memorise without reason.
Base and perpendicular height
The base is one side of the triangle
The perpendicular height meets the base at a right angle
The height gives the other measurement needed for the formula
The height is not always another side of the triangle
Students often choose a sloping side instead of the perpendicular height. Emphasise the right-angle marker.
The base can be in any direction
The base is not always horizontal
A triangle can be turned and the formula stays the same
Choose one side as the base
Use the perpendicular height to that base
This addresses orientation. Rotating a triangle does not change its area.
Right-angled and other triangles
In a right-angled triangle, the two sides that meet at the right angle can be used as base and height
In other triangles, the perpendicular height may be drawn inside or outside the shape
The formula is still A = ½ × b × h
Mention that for non-right-angled triangles, the perpendicular height may need to be extended from the base line.
What is the correct formula for the area of a triangle?
b × h
½ × b × h
2 × b × h
b + h
Distractors reflect common errors: forgetting the half, doubling, or adding instead of multiplying.
Triangle area facts
The area of a triangle is half the area of a matching rectangle. In the formula, base is one side, and the perpendicular height meets it at a right angle.
Reinforces why the formula includes one half and identifies the correct height.
Why can the base of a triangle be in any direction?
Expected answer elements: rotating a triangle does not change its area; the base can be any side; the height must be the perpendicular distance to that base, not just a sloping side.
What is one thing you will remember from this lesson?
Invite short reflections on the most important idea learned, such as square units, same units first, splitting compound shapes, or perpendicular height.
What helped you understand area best today?
Look for metacognitive comments about visuals, worked examples, formulas, or comparing methods.
Glossary
area - the amount of space inside a shape
rectangle - a four-sided shape with four right angles
square units - units used for area, such as cm², m² and mm²
compound shape - a shape made by joining simpler shapes together
triangle - a shape with three sides
formula - a rule written using numbers and symbols
congruent - exactly the same shape and size
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Glossary
base - the side chosen for a triangle when using the area formula
perpendicular - meeting at a right angle of 90°
perpendicular height - the shortest distance from the base to the opposite vertex, measured at a right angle
orientation - the way a shape is turned or positioned
length - one measurement of a rectangle
width - the other measurement of a rectangle
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