Lesson Notes By Weeks and Term v5 - Grade 5
Measurement: perimeter, area and volume (Grade 5) – Week 5 focus
Download the Lessonotes Mobile South Africa app for faster lesson access on Android and iPhone.
Measurement: perimeter, area and volume (Grade 5) – Week 5 focus
Download the Lessonotes Mobile South Africa app for faster lesson access on Android and iPhone.
Subject: Mathematics
Class: Grade 5
Term: 3rd Term
Week: 5
Theme: General lesson support
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.
Measurement is a fundamental skill in mathematics, crucial for everyday life. Understanding perimeter, area, and volume allows us to solve practical problems like fencing a garden, calculating the space needed for a room, or determining how much liquid a container can hold. In South Africa, these skills are essential for tasks ranging from small-scale farming to construction and even cooking! For example, knowing the area helps a farmer determine how much fertilizer to buy or helps a homeowner decide how much paint they need. This week, we will be focusing on consolidating our understanding of these concepts.
Perimeter The perimeter is the total distance around the outside of a two-dimensional shape. It's like walking along the edge of a field – the total distance you walk is the perimeter.
Square: A square has four equal sides. If each side has length s, then the perimeter is P = 4s.
Rectangle: A rectangle has two pairs of equal sides: length (l) and breadth (b). The perimeter is P = 2l + 2b.
Triangle: The perimeter of a triangle is the sum of the lengths of its three sides. If the sides have lengths a, b, and c, then the perimeter is P = a + b + c.
Example 1: A square vegetable garden A farmer in Limpopo wants to fence a square vegetable garden to keep out goats. Each side of the garden is 5 meters long. How much fencing does the farmer need?
Solution: The garden is a square, so the perimeter is P = 4s. s = 5 m, so P = 4 5 m = 20 m. The farmer needs 20 meters of fencing.
Example 2: A rectangular classroom A classroom in Gauteng is 8 meters long and 6 meters wide. What is the perimeter of the classroom floor?
Solution: The classroom floor is a rectangle, so the perimeter is P = 2l + 2b. l = 8 m and b = 6 m, so P = 2 8 m + 2 6 m = 16 m + 12 m = 28 m. The perimeter of the classroom floor is 28 meters.
Example 3: A triangular flower bed A flower bed in a Cape Town park is triangular in shape. The sides are 3 m, 4 m and 5 m. Find the perimeter of the flower bed.
Solution: The perimeter of a triangle is the sum of the lengths of its sides. P = a + b + c P = 3m + 4m + 5m = 12m The perimeter of the flower bed is 12m. Area The area is the amount of surface a two-dimensional shape covers. It's like measuring the amount of carpet needed to cover a floor. We measure area in square units, such as square centimetres (cm²) or square meters (m²).
Square: The area of a square with side s is A = s².
Rectangle: The area of a rectangle with length l and breadth b is A = l x b.
Example 4: A rectangular plot of land A family in KwaZulu-Natal owns a rectangular plot of land that is 12 meters long and 8 meters wide. What is the area of the plot?
Solution: The plot is rectangular, so the area is A = l x b. l = 12 m and b = 8 m, so A = 12 m x 8 m = 96 m². The area of the plot is 96 square meters.
Example 5: Tiling a square floor A square bathroom floor has sides of 3 meters. How many square meters of tiles are needed to cover the floor?
Solution: The floor is a square, so the area is A = s². s = 3 m, so A = (3 m)² = 9 m². You need 9 square meters of tiles. Volume The volume is the amount of space a three-dimensional object occupies. It's like measuring how much water a bottle can hold. We measure volume in cubic units, such as cubic centimetres (cm³) or cubic meters (m³). For a rectangular prism (cuboid), the volume is calculated as: Volume (V) = Length (l) x Breadth (b) x Height (h)
Example 6: A brick A brick is 20 cm long, 10 cm wide, and 5 cm high. What is the volume of the brick?
Solution: The brick is a rectangular prism, so the volume is V = l x b x h. l = 20 cm, b = 10 cm, and h = 5 cm, so V = 20 cm x 10 cm x 5 cm = 1000 cm³. The volume of the brick is 1000 cubic centimetres.
Example 7: A water tank A rectangular water tank is 2 m long, 1 m wide and 1.5 m high. What is the volume of water the tank can hold?
Solution: The water tank is a rectangular prism, so the volume is V = l x b x h. l = 2 m, b = 1 m, and h = 1.5 m, so V = 2 m x 1 m x 1.5 m = 3 m³. The volume of the tank is 3 cubic meters. Guided Practice (With Solutions)
Question 1: A rectangular garden is 7 meters long and 4 meters wide. a) What is the perimeter of the garden? b) What is the area of the garden?
Solution: a)
Perimeter: The formula for the perimeter of a rectangle is P = 2l + 2b. Here, l = 7 m and b = 4 m. P = (2 x 7 m) + (2 x 4 m) = 14 m + 8 m = 22 m. The perimeter of the garden is 22 meters. b)
Area: The formula for the area of a rectangle is A = l x b. Here, l = 7 m and b = 4 m. A = 7 m x 4 m = 28 m². The area of the garden is 28 square meters.
Question 2: A square tile has sides of 20 cm. a) What is the perimeter of the tile? b) What is the area of the tile?
Solution: a)
Perimeter: The formula for the perimeter of a square is P = 4s. Here, s = 20 cm. P = 4 x 20 cm = 80 cm. The perimeter of the tile is 80 cm. b)
Area: The formula for the area of a square is A = s². Here, s = 20 cm. A = (20 cm)² = 20 cm x 20 cm = 400 cm². The area of the tile is 400 square centimetres.
Question 3: A lunch box is in the shape of a rectangular prism. It has a length of 25cm, a width of 15 cm and a height of 8cm. What is the volume of the lunch box?
Solution: The volume of a rectangular prism is V = l x b x h. Here, l = 25 cm, b = 15 cm and h = 8 cm. V = 25 cm x 15 cm x 8 cm = 3000 cm³. The volume of the lunch box is 3000 cubic centimetres. Independent Practice (Questions Only) A farmer has a rectangular field that is 50 m long and 30 m wide. What is the perimeter and area of the field? A square window has sides of 1.5 meters. Calculate the perimeter and area of the window.