Primary 5 Maths: Area of Triangles, Parallelograms and Trapeziums

Primary 5 Maths: Area of Triangles, Parallelograms and Trapeziums — Tutor Lesson Plan

2026-10-27

Tutor lesson-prep guides · Primary maths

Two failures dominate: forgetting to halve the triangle, and using the slant side as the height. This lesson shows where the formulas come from, then drills “which line is the height”.

Objectives — the student can explain each formula from a rectangle, identify the matching base and height on a diagram, and work backwards from an area to a missing height.

01 Prerequisites (3-minute check)

If any of these fails, fix it before the lesson starts.

Skill	Quick check	Pass mark
Rectangle area	Length 8 cm, width 5 cm	40 cm², with units
Multiplication and division	96 ÷ 2	48
Parallel lines	Is the distance between parallel lines constant?	Yes

02 Lesson flow (45 minutes)

Time	Stage	Tutor does	Student does
0-6 min	Cut and rearrange	Cut a parallelogram into a rectangle	Cut along and check the area is unchanged
6-16 min	Three formulas	Derive parallelogram, triangle, trapezium	Write each formula and its origin
16-26 min	Choose the height	Three diagrams: which line is the height?	Mark the right angle on each
26-36 min	Practice	Three questions including one backwards	Work alone, write the formula line
36-42 min	Fix errors	Board the slant-side error	Say which step failed
42-45 min	Exit check	Three questions marked at once	Finish alone

03 Teaching script (read it out)

Scene 1: Parallelogram is a rectangle

Cut the triangle on the left and move it to the right: you get a rectangle.
Length equals base, width equals height, so area = base × height.

Repeat: “The area did not change, so base times height is the area.”

Scene 2: Triangle is half of it

Two identical triangles make one parallelogram, so one triangle is base × height ÷ 2.
The ÷2 comes from there, it is not a rule to memorise.

Student points at the base and the height and says “the height is perpendicular”.

Scene 3: Trapezium is half of a bigger parallelogram

Two identical trapeziums make a parallelogram with base (a + b) and the same height.
So area = (a + b) × height ÷ 2.

Warn: the trapezium also needs ÷2; students often halve only triangles.

04 Question types and worked steps

Type	Example	Steps	Answer
Triangle	base 8, height 5	8 × 5 ÷ 2	20 cm²
Parallelogram	base 7, height 4	7 × 4	28 cm²
Trapezium	a = 6, b = 10, height 4	(6 + 10) × 4 ÷ 2	32 cm²
Backwards	triangle area 30, base 10	30 × 2 ÷ 10	height 6

Sanity check (teach this): A triangle is always half the parallelogram with the same base and height; if it comes out bigger, the ÷2 was dropped or the slant side was used.

05 Independent practice (3 questions)

Question	Answer	What to watch
Triangle base 12, height 7	42 cm²	Halving and units
Parallelogram base 9, height 6	54 cm²	Using the slant side?
Trapezium a = 5, b = 9, height 8	56 cm²	Adding both bases

06 Common mistakes and what to say

Mistake	Student writes	Say this
Triangle not halved	8 × 5 = 40	A triangle is half the parallelogram: divide by 2.
Slant side used as height	7 × 5 on the slant	The height is perpendicular to the base, marked with a right angle.
Trapezium not halved	(6 + 10) × 4 = 64	Trapeziums also divide by 2.
Wrong unit	answer in cm	Area is in square centimetres.

07 Homework (paper, section and question numbers)

Primary 5 first-term paper — Section C, questions 1 to 5
Primary 5 second-term paper — Section C, questions 1 to 4

08 Exit check (last 5 minutes)

Question	Answer	Decision
Triangle base 15, height 8	60 cm²	All right: move to volume
Trapezium a = 4, b = 8, height 5	30 cm²	One wrong: re-teach that formula
Triangle area 48, base 12: height?	8 cm	Two wrong: repeat the cutting activity

09 Tutor FAQ

Is the cutting activity necessary?

Yes. It takes five minutes and answers “where does the ÷2 come from” once and for all.

Students cannot find the height.

Look for the right-angle mark first, then the base it touches; with no mark, ask for the perpendicular distance.

Do you teach composite shapes?

Not here. Composite shapes need all three formulas solid first.

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A TutorZone lesson-prep guide. Written by the TutorZone team; questions and lesson flow are original and are not taken from any school or publisher material.