Lesson Notes By Weeks and Term v5 - Grade 11

Lesson Video

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Performance objectives

• Calculate perimeter of 2D shapes in real-world contexts.
• Calculate area of 2D shapes in real-world contexts.
• Calculate volume of 3D shapes in real-world contexts.
• Apply these calculations to solve practical problems.
• Convert between different metric units of measurement.

Lesson summary

Mathematical Literacy is about applying mathematical skills to real-life situations. This week, we're focusing on measurement – specifically, perimeter, area, and volume. These concepts are crucial for everyday tasks like calculating how much fencing you need for your yard, figuring out the paint needed for a room, or determining the amount of water a JoJo tank can hold. Understanding these measurements empowers you to make informed decisions about your resources and finances, which is especially important in the South African context.

Lesson notes

Perimeter: The perimeter is the total distance around the outside of a two-dimensional shape. Think of it as walking along the edge of a field; the total distance you walk is the perimeter.

Rectangle: Perimeter = 2 (length + width) or P = 2(l + w)

Square: Perimeter = 4 side or P = 4s (since all sides are equal)

Triangle: Perimeter = side1 + side2 + side3 or P = a + b + c Circle: Perimeter (also called circumference) = 2 π * radius or C = 2πr, where π (pi) is approximately 3.142 Area: The area is the amount of surface a two-dimensional shape covers. Imagine you are painting a wall; the area is the total space you need to paint.

Rectangle: Area = length width or A = l * w Square: Area = side side or A = s² Triangle: Area = ½ base * height or A = ½bh Circle: Area = π radius² or A = πr² Volume: The volume is the amount of space a three-dimensional object occupies. Think of filling a container with water; the volume is the amount of water the container can hold.

Cube: Volume = side side * side or V = s³ Rectangular Prism (cuboid): Volume = length width height or V = l w * h Cylinder: Volume = π radius² * height or V = πr²h Units of Measurement: It's vital to use the correct units!

Perimeter: mm, cm, m, km Area: mm², cm², m², km² Volume: mm³, cm³, m³, liters (L), milliliters (ml)

Conversion Factors (Metric System): 1 cm = 10 mm 1 m = 100 cm = 1000 mm 1 km = 1000 m 1 L = 1000 ml

Worked example

Fencing a Garden: A farmer wants to fence a rectangular vegetable garden that is 15 meters long and 8 meters wide. How much fencing does he need?

Solution: The amount of fencing needed is the perimeter of the garden.

Perimeter = 2(l + w) = 2(15m + 8m) = 2(23m) = 46m

Answer: The farmer needs 46 meters of fencing.

Painting a Wall: Thando wants to paint a wall in her room. The wall is 3 meters high and 4 meters wide. A can of paint covers 10 square meters. How many cans of paint does she need?

Solution: First find the area of the wall.

Area = l w = 4m * 3m = 12 m²

Now divide the total area by the area covered by one can of paint.

Number of cans = 12 m² / 10 m²/can = 1.2 cans

Since you can't buy 0.2 of a can, Thando needs to buy 2 cans of paint.

Answer: Thando needs 2 cans of paint.

Water Tank Volume: A cylindrical water tank has a radius of 0.7 meters and a height of 1.5 meters. What is the volume of the tank in liters?

Solution:

Volume = πr²h = 3.142 (0.7m)² 1.5m = 3.142 0.49 m² * 1.5m = 2.31 m³ (approximately)

Now convert cubic meters to liters. 1 m³ = 1000 L

Volume in liters = 2.31 m³ 1000 L/m³ = 2310 L

Answer: The volume of the tank is approximately 2310 liters.

Guided Practice (With Solutions)

Question: A square piece of land has sides of 25 meters. Calculate the length of fencing required to enclose the land.

Solution:

Shape: Square

Formula: Perimeter = 4 side

Calculation: Perimeter = 4 25m = 100m

Answer: 100 meters of fencing is required.

Question: A rectangular room is 6 meters long and 4 meters wide. Calculate the area of the floor that needs to be covered with tiles.

Solution:

Shape: Rectangle

Formula: Area = length width

Calculation: Area = 6m 4m = 24 m²

Answer: 24 square meters of tiles are needed.

Question: A cylindrical can of beans has a radius of 4 cm and a height of 10 cm. Calculate the volume of beans the can can hold.

Solution:

Shape: Cylinder

Formula: Volume = π radius² * height

Calculation: Volume = 3.142 (4cm)² 10cm = 3.142 16 cm² * 10 cm = 502.72 cm³

Answer: The can can hold approximately 502.72 cubic centimeters of beans.

Question: Calculate the area of a triangular piece of land with a base of 12m and a perpendicular height of 8m.

Solution:

Shape: Triangle

Formula: Area = ½ base * height

Calculation: Area = ½ 12m * 8m = 48 m²

Answer: The area of the land is 48 square meters.

Independent Practice (Questions Only)

A rectangular swimming pool is 10 meters long and 5 meters wide. What is the perimeter of the pool?

What is the area of a circular table with a diameter of 1.2 meters?

A rectangular prism (box) has a length of 20 cm, a width of 15 cm, and a height of 8 cm. Calculate its volume.

A circular flower bed has a radius of 3 meters. What is the area of the flower bed?

Calculate the perimeter of a triangle with sides of 7 cm, 9 cm, and 11 cm.

A water tank is in the shape of a cube with sides of 1.5 meters. What is the volume of the tank in liters?

Nomusa wants to make a tablecloth for a rectangular table that is 1.8m long and 1.2m wide. She wants the tablecloth to overhang the table by 20cm on each side. What are the dimensions of the tablecloth she needs to make? What is the area of the tablecloth?

A farmer needs to apply fertilizer to a square field that is 50m by 50m. The fertilizer instructions say to apply 2kg of fertilizer for every 100 square meters. How much fertilizer does the farmer need in total?

Convert 5.4 m³ to litres.

Calculate the perimeter and the area of your maths textbook.