Lesson Notes By Weeks and Term v3 - Primary 5
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 5
Term: 3rd Term
Week: 9
Theme: Mensuration And Geometry
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.
Pupils should be able to calculate the area of a right angle triangle.
2. 1.
Recap of Area: Area is the amount of surface a two-dimensional shape covers. It is measured in square units (e.g., square centimetres (cm2), square metres (m2)). Previously, pupils would have learned that: Area of a square = side × side Area of a rectangle = length × breadth (or base × height) 2.
2. Understanding a Right-Angled Triangle: A right-angled triangle is a triangle that has one internal angle exactly equal to 90 degrees (a right angle). The side opposite the right angle is called the hypotenuse (it is always the longest side). The other two sides are often referred to as the base and the height (or perpendicular height), as they meet at the right angle. The choice of which is the base and which is the height depends on the orientation, but they are the two sides forming the right angle. 2.
3. Deriving the Formula for the Area of a Right-Angled Triangle: The formula for the area of a right-angled triangle can be easily derived from the area of a rectangle. Consider a rectangle with length (L) and breadth (B). Its area is L × B. If this rectangle is cut diagonally from one corner to the opposite corner, it forms two identical right-angled triangles. Each of these triangles has a base equal to the length (L) of the rectangle and a height equal to the breadth (B) of the rectangle. Since the rectangle is divided into two equal triangles, the area of one right-angled triangle must be half the area of the rectangle.
Therefore: Area of a right-angled triangle = (1/2) × Area of rectangle Area of a right-angled triangle = (1/2) × length × breadth Replacing 'length' with 'base' and 'breadth' with 'height' (which are the perpendicular sides in a right-angled triangle): Formula: Area of a Right-Angled Triangle = (1/2) × base × height Key points to note for teachers: The 'base' and 'height' must be the two sides that form the right angle. Units for area are always square units (e.g., cm2, m2, km2). Worked
Examples: Example 1: A carpenter needs to cut a triangular piece of wood for a roof support. The two sides forming the right angle measure 8 cm and 6 cm. Calculate the area of the wood piece.
Solution: Identify the base and height: Base = 8 cm, Height = 6 cm.
Recall the formula: Area = (1/2) × base × height Substitute the values: Area = (1/2) × 8 cm × 6 cm Calculate: Area = (1/2) × 48 cm2 Area = 24 cm2 Example 2: A farmer has a small triangular yam plot near the river. The two sides meeting at a right angle are 15 metres and 20 metres long. Find the area of the yam plot.
Solution: Identify the base and height: Base = 15 m, Height = 20 m.
Recall the formula: Area = (1/2) × base × height Substitute the values: Area = (1/2) × 15 m × 20 m Calculate: Area = (1/2) × 300 m2 Area = 150 m2 Example 3: Calculate the area of a right-angled triangle whose perpendicular sides are 12 cm and 5 cm.
Solution: Identify the base and height: Base = 12 cm, Height = 5 cm.
Recall the formula: Area = (1/2) × base × height Substitute the values: Area = (1/2) × 12 cm × 5 cm Calculate: Area = (1/2) × 60 cm2 Area = 30 cm2 3.
1. Introduction (5-10 minutes): Teacher Activity: Begin by reviewing the concept of area for squares and rectangles. Ask pupils questions like, "What is area?" and "How do we find the area of a square/rectangle?" Display simple diagrams of squares and rectangles and ask pupils to state their areas if given dimensions.
Pupil Activity: Pupils recall and discuss the concept of area and the formulas for squares and rectangles. They answer questions and participate in a brief recap session. 3.
2. Presentation (20-25 minutes): Teacher Activity: Introduce the term "right-angled triangle." Draw one on the board and point out the right angle, the base, and the height (the two sides forming the right angle).
Demonstrate the derivation of the formula: Show a rectangular cardboard cut-out. Measure and state its length and breadth. Calculate and state its area. Draw a diagonal line on the rectangle, cutting it into two. Ask pupils what shapes are formed (two triangles). Cut the rectangle along the diagonal to show two separate right-angled triangles. Ask pupils to observe if the two triangles are identical. Lead them to conclude that the area of one right-angled triangle is half the area of the original rectangle. From this, explicitly state the formula: Area = (1/2) × base × height. Explain clearly that the 'base' and 'height' in the formula refer to the two sides that meet at the right angle. Work through Example 1 (carpenter's wood piece) step-by-step on the board, ensuring clarity on calculation and units.
Pupil Activity: Pupils observe the demonstration with the cut-out shapes. They actively participate in deducing the formula by answering guiding questions. Pupils copy the formula and the worked example into their notebooks. They ask clarifying questions as needed. 3.
3. Guided Practice (10-15 minutes): Teacher Activity: Present Example 2 (farmer's yam plot) and Example 3 on the board. Guide pupils to solve them collaboratively. Ask pupils to identify the base and height, state the formula, substitute values, and calculate. Emphasise writing down steps and correct units.
Pupil Activity: Pupils work in pairs or individually to solve the guided practice problems, guided by the teacher. They share their answers and compare methods. Corrections are made as a class. 3.
4. Class Discussion and Reinforcement (5 minutes): Teacher Activity: Ask pupils to explain the formula in their own words. Address any misconceptions (e.g., confusing base/height with the hypotenuse). Emphasize the importance of correct units.
Pupil Activity: Pupils articulate their understanding and ask any remaining questions.
Question 1: A tailor is cutting a triangular piece of fabric for a dress design. The two sides that form the right angle are 10 cm and 7 cm long. What is the area of the fabric piece?
Solution: Identify Base and Height: Base = 10 cm Height = 7 cm State the Formula: Area of a right-angled triangle = (1/2) × base × height Substitute Values: Area = (1/2) × 10 cm × 7 cm Calculate: Area = (1/2) × 70 cm2 Area = 35 cm2
Commentary: This question directly applies the formula with straightforward values, suitable for initial practice.
Question 2: Mr. Ade owns a small plot of land shaped like a right-angled triangle. Its perpendicular sides are 24 meters and 15 meters. Calculate the area of his land.
Solution: Identify Base and Height: Base = 24 m Height = 15 m State the Formula: Area of a right-angled triangle = (1/2) × base × height Substitute Values: Area = (1/2) × 24 m × 15 m Calculate: Area = (1/2) × 360 m2 Area = 180 m2
Commentary: This question uses slightly larger numbers and a different unit (meters) to ensure pupils can handle various numerical inputs and correctly apply units.
Question 3: Find the area of the right-angled triangular part of a building's gable, where the base is 9 meters and the vertical height (perpendicular to the base) is 4 meters.
Solution: Identify Base and Height: Base = 9 m Height = 4 m State the Formula: Area of a right-angled triangle = (1/2) × base × height Substitute Values: Area = (1/2) × 9 m × 4 m Calculate: Area = (1/2) × 36 m2 Area = 18 m2
Commentary: This question uses a real-world scenario (gable of a building) and reinforces identifying the perpendicular sides as base and height. 8.
1. Remediation (for struggling learners): Concrete Manipulatives: Provide pupils with more physical rectangular cut-outs that they can personally cut along the diagonal to form two right-angled triangles. This hands-on experience reinforces the "half a rectangle" concept.
Visual Aids: Use large, clear diagrams on the board or flashcards that explicitly label the base and height of right-angled triangles, ensuring they identify the sides forming the right angle.
Simplistic Values: Start with very simple numbers (e.g., base 2 cm, height 4 cm) to minimise calculation difficulty, allowing them to focus on understanding the formula and steps.
Peer Tutoring: Pair struggling learners with more capable peers for one-on-one explanation and support during guided practice.
Step-by-Step Prompts: Provide worksheets with the formula and steps already written out, requiring pupils only to fill in the numbers. 8.
2. Extension (for high-achieving learners): Problem Solving: Present word problems that require an extra step beyond simple calculation, e.g., "If the area of a right-angled triangle is 50 cm2 and its base is 10 cm, what is its height?" (This introduces working backward or algebraic thinking).
Compound Shapes: Challenge them to find the area of composite shapes that include right-angled triangles (e.g., a shape made of a rectangle and a right-angled triangle attached to one side).
Real-world Scenarios: Encourage them to research or imagine more complex real-life scenarios in Nigeria where the area of right-angled triangles would be useful (e.g., calculating the amount of paint needed for a uniquely shaped triangular signpost, or the surface area of a complex roof structure).
Unit Conversion: Introduce problems that require converting units before calculation (e.g., base in cm, height in m, then calculate area in cm2).
Example 1:
A carpenter needs to cut a triangular piece of wood for a roof support. The two sides forming the right angle measure 8 cm and 6 cm. Calculate the area of the wood piece.
Solution:
Identify the base and height: Base = 8 cm, Height = 6 cm.
Recall the formula: Area = (1/2) × base × height
Substitute the values: Area = (1/2) × 8 cm × 6 cm
Calculate: Area = (1/2) × 48 cm²
Area = 24 cm²
Example 2:
A farmer has a small triangular yam plot near the river. The two sides meeting at a right angle are 15 metres and 20 metres long. Find the area of the yam plot.
Solution:
Identify the base and height: Base = 15 m, Height = 20 m.
Recall the formula: Area = (1/2) × base × height
Substitute the values: Area = (1/2) × 15 m × 20 m
Calculate: Area = (1/2) × 300 m²
Area = 150 m²
Land Measurement and Farming (Agriculture): In rural and peri-urban Nigeria, land plots are often irregular. Knowledge of the area of right-angled triangles helps farmers accurately estimate the size of their plots, especially those bordering streams or roads that create triangular sections. This helps in determining how much fertilizer, seeds, or labour is needed for a specific section of their farm. For example, a farmer in Benue State (often called "Food Basket of the Nation") might need to calculate the area of a triangular section of his yam farm to plan his planting. Construction and Carpentry (Vocational Skills): Local builders and carpenters frequently encounter triangular shapes. Roof gables (the triangular section of a wall between the edges of a sloping roof) are often right-angled. Understanding how to calculate their area allows artisans to accurately estimate the amount of roofing sheets, plywood, or paint required, preventing waste and ensuring cost-effective project execution. A carpenter in Lagos building a house might use this to calculate the materials for the roof truss structure.
Art and Design (Cultural Integration): Many traditional Nigerian art forms and textile designs (e.g., Adire, Aso Oke patterns) incorporate geometric shapes, including triangles. While not directly calculating area during creation, understanding how shapes relate and divide can foster appreciation for geometry in design. More practically, tailors cutting fabric for triangular motifs or details on garments use area estimation to minimise fabric wastage, which is crucial in their trade. For instance, a seamstress in Kano making a traditional gown with triangular inserts.