Area, Trapezium Formula, Land Areas and Hectares for Primary 6

Class: Primary 6
Term: 2nd Term
Week: 10
Age: 11 years
Duration: 45 minutes
Subject: General Mathematics
Curriculum Theme: Geometry and Measurement
Previous Lesson: Perimeter, Rectangle Perimeters and Comparing Equal Areas.
Topic: AREA
Subject Matter: Area of trapezium by splitting into rectangle and triangle, formula for area of trapezium as 1/2(a+b)h, worked examples on trapezium area, land areas in square metres, converting square metres to hectares.

Specific Objectives

By the end of the lesson, pupils should be able to:

Cognitive Domain:

• Define a trapezium.
• State the formula for calculating the area of a trapezium.
• Calculate the area of a trapezium using the formula.
• Convert land areas from square metres to hectares and vice versa.

Affective Domain:

• Appreciate the importance of calculating area in real-life situations.
• Participate actively in class discussions and problem-solving.

Psychomotor Domain:

• Draw a trapezium and show how it can be split into a rectangle and a triangle.
• Accurately solve problems involving the area of a trapezium and land area conversions.

Social Domain:

• Work cooperatively with classmates to solve mathematical problems.

Reference Materials

The following resources were used in planning this lesson:

• 9 Years Basic Education Curriculum (Primary 4-6)
• State Unified Scheme of Work (Primary 6)
• Primary Mathematics for Nigerian Schools, Pupil’s Book 6
• https://www.mathsisfun.com/geometry/trapezoid-area.html
• https://byjus.com/maths/area-of-trapezium/

Instructional Materials

The teacher will teach this lesson with the aid of:

• Textbook
• Workbook
• Formula book
• Charts showing different types of quadrilaterals
• Chart illustrating a trapezium split into a rectangle and a triangle
• Ruler and protractor

Rationale for the Lesson

This lesson helps pupils understand how to calculate the area of a trapezium, a common shape found in buildings and land plots. Knowing how to calculate land areas and convert units like square metres to hectares is important for understanding property sizes and environmental planning in daily life.

Prerequisite/Previous Knowledge

Pupils have prior knowledge of calculating the area of rectangles and triangles, and basic understanding of quadrilaterals.

Lesson Content/Board Summary

Area of Trapezium and Land Area

What is a Trapezium?

A trapezium (also known as a trapezoid) is a quadrilateral (a four-sided polygon) that has at least one pair of parallel sides.

The parallel sides are called the bases, and the perpendicular distance between them is the height.

Area of Trapezium by Splitting into Rectangle and Triangle

A trapezium can be split into simpler shapes like a rectangle and one or two triangles. The total area of the trapezium is the sum of the areas of these simpler shapes.

For example, a trapezium can be split into a rectangle and a right-angled triangle (if one of the non-parallel sides is perpendicular to the bases) or a rectangle and two triangles (if neither non-parallel side is perpendicular).

Formula for the Area of a Trapezium

The area of a trapezium can be calculated using the formula:

Area (A) = 1/2 × (a + b) × h

Where:

• a and b are the lengths of the two parallel sides (bases).
• h is the perpendicular height (the distance between the parallel sides).

Worked Examples on Trapezium Area

Example 1: Find the area of a trapezium with parallel sides 7 cm and 11 cm, and a height of 4 cm.

Solution:

Step 1: Write down the formula.

A = 1/2 × (a + b) × h

Step 2: Identify the given values.

a = 7 cm, b = 11 cm, h = 4 cm

Step 3: Substitute the values into the formula.

A = 1/2 × (7 + 11) × 4

Step 4: Perform the addition inside the bracket.

A = 1/2 × (18) × 4

Step 5: Multiply the values.

A = 1/2 × 72

A = 36 cm²

The area of the trapezium is 36 cm².

Example 2: A trapezium has an area of 50 m². If its parallel sides are 8 m and 12 m, find its height.

Solution:

Step 1: Write down the formula.

A = 1/2 × (a + b) × h

Step 2: Identify the given values.

A = 50 m², a = 8 m, b = 12 m

Step 3: Substitute the values into the formula.

50 = 1/2 × (8 + 12) × h

Step 4: Perform the addition inside the bracket.

50 = 1/2 × (20) × h

Step 5: Simplify the right side.

50 = 10 × h

Step 6: Solve for h by dividing both sides by 10.

h = 50 / 10

h = 5 m

The height of the trapezium is 5 m.

Land Areas in Square Metres (m²)

Land areas are often measured in square metres (m²). This unit represents the area of a square with sides of 1 metre each.

Converting Square Metres to Hectares

Hectare (ha) is a unit of area commonly used for measuring land, especially in agriculture and forestry. It is a larger unit than the square metre.

Conversion Factor:

• 1 Hectare (ha) = 10,000 square metres (m²)

NOTE:

• To convert from square metres (smaller unit) to hectares (larger unit), you divide by 10,000.
• To convert from hectares (larger unit) to square metres (smaller unit), you multiply by 10,000.

Worked Examples on Land Area Conversion

Example 1: Convert 45,000 m² to hectares.

Solution:

Step 1: Identify the conversion factor.

1 ha = 10,000 m²

Step 2: Divide the given square metres by the conversion factor to get hectares.

Hectares = 45,000 m² ÷ 10,000 m²/ha

Hectares = 4.5 ha

So, 45,000 m² is equal to 4.5 hectares.

Example 2: Convert 3.2 hectares to square metres.

Solution:

Step 1: Identify the conversion factor.

1 ha = 10,000 m²

Step 2: Multiply the given hectares by the conversion factor to get square metres.

Square metres = 3.2 ha × 10,000 m²/ha

Square metres = 32,000 m²

So, 3.2 hectares is equal to 32,000 square metres.

Teaching Methods/Instructional Techniques

Discussion, Lecture, Demonstration, Question and Answer, Visual Aids

Instructional Procedures

Step 1: Introduction

Time: 3 minutes

Teaching Skill: Set Induction

Teacher’s Activity: The teacher greets the pupils and asks them to recall different types of quadrilaterals they know (e.g., square, rectangle, parallelogram). The teacher then introduces the topic of “Area of Trapezium and Land Area” by showing a picture of a field or a roof shape that resembles a trapezium.

Pupils’ Activity: Pupils respond to the teacher’s questions and observe the pictures.

Learning Point: Pupils recall previous knowledge of quadrilaterals and are introduced to the lesson topic.

Step 2: Definition and Splitting a Trapezium

Time: 7 minutes

Teaching Skill: Explanation/Demonstration

Teacher’s Activity: The teacher defines a trapezium and explains its key features (parallel sides, height). Using a chart or whiteboard, the teacher demonstrates how a trapezium can be split into a rectangle and one or two triangles to help visualize its area derivation.

Pupils’ Activity: Pupils listen attentively, observe the demonstration, and may draw a trapezium in their notebooks.

Learning Point: Pupils understand the definition and visual representation of a trapezium.

Step 3: Trapezium Formula and Worked Examples

Time: 12 minutes

Teaching Skill: Explanation/Problem Solving

Teacher’s Activity: The teacher introduces the formula for the area of a trapezium: A = 1/2 × (a + b) × h, explaining each variable. The teacher then works through Example 1 and Example 2 from the board summary, guiding pupils through each step on the board. The teacher ensures pupils understand how to apply the formula and how to solve for an unknown variable like height.

Pupils’ Activity: Pupils copy the formula and worked examples into their notebooks, asking questions for clarification.

Learning Point: Pupils learn to apply the area formula for a trapezium and solve related problems.

Step 4: Land Areas in Square Metres

Time: 5 minutes

Teaching Skill: Explanation

Teacher’s Activity: The teacher explains that large areas of land are measured in square metres (m²). The teacher discusses practical scenarios where land area measurement is needed, such as for farms, plots of land, or construction sites.

Pupils’ Activity: Pupils listen and understand the concept of land areas measured in square metres.

Learning Point: Pupils understand the unit for measuring land areas.

Step 5: Conversion of Square Metres to Hectares (Explanation)

Time: 5 minutes

Teaching Skill: Explanation

Teacher’s Activity: The teacher introduces the hectare (ha) as a larger unit for land measurement and explains the conversion factor: 1 hectare = 10,000 m². The teacher emphasizes when to multiply and when to divide during conversion.

Pupils’ Activity: Pupils copy the conversion factor and notes on when to multiply or divide into their notebooks.

Learning Point: Pupils understand the hectare unit and the basic rule for conversion.

Step 6: Worked Examples on Land Area Conversion and Practice

Time: 8 minutes

Teaching Skill: Demonstration/Problem Solving

Teacher’s Activity: The teacher guides pupils through Example 1 and Example 2 for land area conversion from the board summary. The teacher then provides a few quick practice questions for pupils to attempt individually or in pairs to reinforce the conversion process.

Pupils’ Activity: Pupils copy the worked examples and attempt the practice questions given by the teacher.

Learning Point: Pupils learn how to apply the conversion rules between square metres and hectares through practice.

Step 7: Evaluation/Review

Time: 5 minutes

Teaching Skill: Questioning/Assessment

Teacher’s Activity: The teacher evaluates the learning by asking the following questions:

1. Define a trapezium.
2. State the formula for calculating the area of a trapezium.
3. Calculate the area of a trapezium with parallel sides 6 cm and 10 cm, and a height of 3 cm.
4. Convert 35,000 m² to hectares.
5. Convert 2.5 hectares to square metres.

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Pupils demonstrate understanding of the lesson.

Step 8: Conclusion

Time: 0 minutes

Teacher’s Activity: The teacher summarizes the main points of the lesson, reiterating the formula for the area of a trapezium and the conversion between square metres and hectares. The teacher gives an assignment:

Assignment:

1. A trapezium has parallel sides of 9m and 15m, and a height of 7m. Calculate its area.
2. A rectangular plot of land measures 200m by 150m. Calculate its area in square metres and then convert it to hectares.

Pupils’ Activity: Pupils listen to the summary and copy the assignment.

Learning Point: Pupils consolidate their learning and prepare for independent practice.

Home Task: Solve three new exercises on AREA. Show each step and check each answer.

Lesson Keywords

• Trapezium – A quadrilateral with at least one pair of parallel sides.
• Area – The amount of space a flat surface covers.
• Parallel sides – Sides that are always the same distance apart and never meet.
• Height – The perpendicular distance between the parallel sides of a trapezium.
• Square metre (m²) – A unit of area representing a square with sides of 1 metre.
• Hectare (ha) – A unit of land area equal to 10,000 square metres.

Differentiation

For pupils who grasp concepts quickly, the teacher will provide more challenging problems, such as finding the missing length of a parallel side when the area and other dimensions are given. For pupils who require additional support, the teacher will provide simplified diagrams, offer one-on-one guidance, and use concrete examples like cutting out paper trapeziums to demonstrate splitting into simpler shapes.

Note for teachers using this lesson plan

Ensure that pupils understand the concept of perpendicular height in a trapezium. Use visual aids extensively, especially for demonstrating the splitting of a trapezium and for the conversion of units. Encourage pupils to draw diagrams for each problem to help them visualize and correctly identify the parallel sides and height. Emphasize the practical applications of calculating land areas to make the lesson more relevant.