Lesson Notes By Weeks and Term v3 - Primary 6
Area
Download the Lessonotes Mobile Nigeria 2025 app for faster lesson access on Android and iPhone.
Area
Download the Lessonotes Mobile Nigeria 2025 app for faster lesson access on Android and iPhone.
Subject: General Mathematics
Class: Primary 6
Term: 2nd Term
Week: 9
Theme: Measurement
This page supports the lesson note with a companion video and a short classroom-ready summary.
For class groups and homework, share this lesson page so learners also get the summary, objectives, and full lesson context.
Calculate the are as of figure which can be divided in to rectangles and or triangles Calculate land are as in hectares.
Triangle) A farmer wants to calculate the area of his farm plot in Enugu, which has an unusual shape as shown: ``` 15 m +--------+ | | 10 m | | +--------+ \ / 8 m \ / . ``` This is a rectangle joined to a triangle. The base of the triangle is the same as the width of the rectangle. The 8m is the height of the triangle.
Step 1: Decomposition The figure is already decomposed into: Rectangle: Length = 15 m, Width = 10 m.
Triangle: Base = 10 m (same as rectangle's width), Height = 8 m.
Step 2: Calculate Individual Areas Area of Rectangle = Length × Width = 15 m × 10 m = 150 m2 Area of Triangle = 1⁄2 × Base × Height = 1⁄2 × 10 m × 8 m = 5 m × 8 m = 40 m2 Step 3: Sum the Areas Total Area = Area of Rectangle + Area of Triangle = 150 m2 + 40 m2 = 190 m2 D. Calculating Land Areas in Hectares For large areas of land, especially in agriculture, real estate, and surveying in Nigeria, the unit "hectare" is commonly used.
Definition: One hectare (ha) is equal to 10,000 square metres (m2). 1 hectare = 10,000 m2 Conversion Steps: Square Metres to Hectares: Divide the area in m2 by 10,
0
0
0. Area (ha) = Area (m2) / 10,000 Hectares to Square Metres: Multiply the area in hectares by 10,
0
0
0. Area (m2) = Area (ha) × 10,000 Worked Example 3: Converting m2 to Hectares A new cocoa farm in Ondo State has a total area of 250,000 m
2. How many hectares is this?
Step 1: Identify the given area in m
2. Area = 250,000 m2 Step 2: Apply the conversion formula. Area (ha) = Area (m2) / 10,000 Area (ha) = 250,000 m2 / 10,000 = 25 hectares Worked Example 4: Calculating Area in m2 and then converting to Hectares A rectangular piece of land in Abuja is 400 m long and 250 m wide. Calculate its area in hectares.
Step 1: Calculate the area in square metres. Area = Length × Width Area = 400 m × 250 m = 100,000 m2 Step 2: Convert the area from m2 to hectares.** Area (ha) = Area (m2) / 10,000 * Area (ha) = 100,000 m2 / 10,000 = 10 hectares A. Definition of Area Area is the measure of the two-dimensional space occupied by a flat shape or surface. It is expressed in square units (e.g., square centimetres (cm2), square metres (m2), square kilometres (km2)). B. Area of Basic Shapes (Recap) Before tackling composite shapes, learners should be familiar with the area formulas for fundamental shapes: Rectangle: Area = Length × Width (or Breadth).
Example: A rectangular room is 5 m long and 4 m wide. Area = 5 m × 4 m = 20 m
2. Square: Area = Side × Side (since length = width).
Example: A square tile has a side of 30 cm. Area = 30 cm × 30 cm = 900 cm
2. Triangle: Area = 1⁄2 × Base × Height.
Example: A triangular piece of land has a base of 10 m and a height of 6 m. Area = 1⁄2 × 10 m × 6 m = 30 m
2. C. Area of Composite Figures (Figures Divided into Rectangles and/or Triangles) Composite figures are shapes made up of two or more basic geometric shapes. To find their area, the teacher should guide learners through these steps:
1. Decomposition: Divide the complex shape into simpler, non-overlapping rectangles and/or triangles. It is crucial to look for the easiest way to split the figure.
2. Measure Missing Sides: Use the given dimensions to deduce the lengths of any unknown sides that result from the division.
3. Calculate Individual Areas: Find the area of each individual basic shape using the appropriate formula.
4. Sum the Areas: Add up the areas of all the individual basic shapes to get the total area of the composite figure.
Worked Example 1: Composite Shape (Rectangles) Consider the floor plan of a small compound in Kano, shaped as shown below (all angles are right angles): ``` 8 m +---------+ | | 6 m 10 m | | +-----+---+ | | | 4 m | 4 m +-----+ ``` Step 1: Decomposition The figure can be divided into two rectangles, A and B, in two ways: Method 1: A large rectangle (10m x 8m) with a smaller rectangle (4m x 4m) removed from one corner. This is 'subtraction' of areas.
Method 2: Dividing it into two rectangles by extending one of the internal lines. Let's use this method as it's typically easier for Primary
6. Let's divide it horizontally. Draw a line extending from the 4m side to the right, splitting the shape into: Rectangle A: Top rectangle. Its length is 8 m. Its width is 6 m (deduced from the vertical side).
Rectangle B: Bottom rectangle. Its length is 4 m. Its width is 4 m. Alternatively, divide it vertically. Draw a line downwards from the corner of the 8m side.
Rectangle A: The left larger rectangle. Its total height is 10 m. Its width needs to be deduced. The total top width is 8m. The bottom part of the right side is 4m. This means the width of the larger rectangle on the left is 8m - 4m = 4m. (This deduction is critical). So, Rectangle A is 10m x 4m.
Rectangle B: The right smaller rectangle. Its width is 4 m. Its height is 4 m. Let's use the horizontal division for clarity: ``` 8 m +-----------------+ | A | 6 m | | +-----------------+---- | B | | 4 m (total height of right part) +-----------+ 4 m ``` Wait, the initial diagram labels are a bit tricky. Let's re-interpret the diagram as usually presented for composite areas. Corrected interpretation and decomposition: ``` 8 m +---------+ (Top segment width) | | 6 m (Top segment height) 10 m | A | +---------+--- | | 4 m (Bottom segment height) | B | +---------+ (Bottom segment width) 4 m (This is the width of the bottom segment, and 8m is the total width of the top) ``` This implies the shape looks like an "L".
Let's make it clearer: ``` (1) 8 m +-----------------+ | | | Area 1 | 6 m | | +--------+--------+ (Line to presented for composite areas. Corrected interpretation and decomposition: ``` 8 m +---------+ (Top segment width) | | 6 m (Top segment height) 10 m | A | +---------+--- | | 4 m (Bottom segment height) | B | +---------+ (Bottom segment width) 4 m (This is the width of the bottom segment, and 8m is the total width of the top) ``` This implies the shape looks like an "L".
Let's make it clearer: ``` (1) 8 m +-----------------+ | | | Area 1 | 6 m | | +--------+--------+ (Line to divide) | | | Area 2 | 4 m (height of this section) | | +--------+ 4 m ``` Step 1: Decomposition Divide the L-shape into two rectangles: Rectangle 1 (Top): Length = 8 m, Width = 6 m.
Rectangle 2 (Bottom): Length = 4 m. Its height needs to be determined. The total height of the left side is 10 m. The height of Rectangle 1 is 6 m. So, the height of Rectangle 2 is 10 m - 6 m = 4 m. Wait, the diagram shows 10m as the total height of the left side. The 4m is the width of the bottom part. The 6m is the height of the top part. Let's redraw the common L-shape for clarity: ``` 8m +-------+ | | | A | 6m | | +---+---+-- | B | 4m (height of B) +---+ 4m (width of B) ``` This diagram is ambiguous with the 10m label. Let's use the standard "L" shape where all exterior dimensions are given, and some interior are derived.
Assumed L-shape (clearer for P6): ``` 8 m +-------+ | | | A | 6 m | | +-------+------- | | | 4 m | | | +-------+------- 4 m ``` The 10m label is still confusing if 6m and 4m are heights. Assuming the total height of the left vertical line is 10m, and the top segment height is 6m, then the bottom segment height is 4m. And if the total width is 8m, and the bottom segment width is 4m, then the left part of the top segment is 4m. This makes the top rectangle 8m x 6m and the bottom rectangle 4m x 4m. Let's re-evaluate the initial diagram from the problem statement: ``` 8 m +---------+ | | 6 m 10 m | | +-----+---+ | | | 4 m | 4 m +-----+ ``` This diagram is read as: total left height = 10m. Top width = 8m. Top right height = 6m. Bottom width = 4m. Bottom right height = 4m.
Method 1: Division into two rectangles (Horizontal Cut) Draw a horizontal line extending from the bottom-left corner of the upper rectangle.
Rectangle 1 (Top): Length = 8 m, Width = 6 m.
Rectangle 2 (Bottom): Length = 4 m. Its height is the remaining part of the total height. Total height on the left is 10 m. Height of Rectangle 1 is 6 m. So, height of Rectangle 2 = 10 m - 6 m = 4 m. So, Rectangle 2 is 4 m × 4 m.
Step 2: Calculate Individual Areas Area of Rectangle 1 (A) = Length × Width = 8 m × 6 m = 48 m2 Area of Rectangle 2 (B) = Length × Width = 4 m × 4 m = 16 m2 Step 3: Sum the Areas Total Area = Area A + Area B = 48 m2 + 16 m2 = 64 m2 Worked Example 2: Composite Shape (Rectangle and Triangle) A farmer wants to calculate the area of his farm plot in Enugu, which has an unusual shape as shown: ``` 15 m +--------+ | | 10 m | | +--------+ \ / 8 m \ / . ``` This is a rectangle joined to a triangle. The base of the triangle is the same as the width of the rectangle. The 8m is the height of the triangle.
Step 1: Decomposition The figure is already decomposed into: Rectangle: Length = 15 m, Width = 10 m.
Triangle: Materials: Whiteboard/Blackboard, markers/chalk, ruler, pre-drawn diagrams of composite shapes, possibly cut-out paper shapes, measuring tape (optional, for real-world connection). A. Introduction (10 minutes) The teacher reviews the concept of area for basic shapes (rectangle, square, triangle) by asking learners to recall formulas and units. The teacher displays a diagram of an irregular plot of land (a composite shape) and asks learners how they would find its area. This leads to the idea of breaking it down. The teacher introduces the term "composite figures" and explains that they are common in real life (e.g., room layouts, farm plots, design patterns).
B. Development (30 minutes)
Activity 1: Decomposing Composite Shapes (15 minutes) The teacher presents several diagrams of composite shapes on the board (similar to Worked Example 1 and 2 but without values initially). The teacher guides learners to identify the basic shapes (rectangles, triangles) within each composite figure and discusses different ways to divide them. Learners are encouraged to suggest division lines and justify their choices. The teacher provides one or two composite shapes with dimensions and demonstrates step-by-step how to: Divide the shape into basic parts. Determine the dimensions of each part using subtraction/addition of given lengths. Calculate the area of each part. Sum the areas. The teacher uses Worked Example 1 (composite rectangle) and Worked Example 2 (rectangle + triangle) to illustrate.
Activity 2: Understanding and Converting Hectares (15 minutes) The teacher explains that for large areas of land, square metres can be a very large number, and a more convenient unit, the hectare, is used in Nigeria. The teacher clearly defines 1 hectare = 10,000 m
2. The teacher explains the conversion process: m2 to hectares (divide by 10,000) hectares to m2 (multiply by 10,000) The teacher uses Worked Example 3 and 4 to demonstrate the conversion, emphasizing the movement of the decimal point or removal/addition of zeros.
C. Consolidation (10 minutes) The teacher provides a quick recap of the two main skills: calculating the area of composite shapes and converting between m2 and hectares. The teacher addresses any immediate questions or misconceptions. The teacher assigns a quick practice question for learners to attempt individually or in pairs.
Farm Planning and Land Use: Application: A farmer in Sokoto needs to calculate the total area of different sections of his farm (e.g., for rice, maize, groundnuts) to determine how much seed, fertilizer, or irrigation water is required. Many farms in Nigeria are not perfectly rectangular but have irregular boundaries, requiring division into simpler shapes.
Integration: Learners can be asked to draw an irregular farm plot and calculate its area, then discuss how this knowledge helps a farmer manage resources efficiently. For instance, knowing the area in hectares helps in securing agricultural loans or subsidies often calculated per hectare.
Building and Construction: Application: A building contractor in Enugu needs to calculate the area of the floor space of a complex building design (e.g., an L-shaped church or a building with a triangular entrance) to order the correct amount of tiles or cement for screeding.
Integration: Learners can be shown floor plans of actual Nigerian buildings or homes and asked to calculate areas of rooms, understanding how this impacts the cost of materials like tiles, carpets, or paint. They can discuss how different room shapes might affect furniture placement.
Community Development and Surveying: Application: Town planners and land surveyors use area calculations to delineate land boundaries, plan new roads, allocate plots for schools or markets, or determine compensation for land acquisition. These large areas are typically measured in hectares.
Integration: Learners can discuss how accurate land measurement prevents disputes among neighbours or within communities, a common issue in Nigeria. They can explore how government agencies use hectares to describe large development projects, like new housing estates or industrial parks.