Area of Rectangles and Rectangular Farmland for Primary 4

Area of Rectangles and Rectangular Farmland

Performance Objectives

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

1. find area of rectangles using the formula;
2. calculate the area of rectangular farmland in the environment;
3. solve problems on quantitative aptitude related to areas of rectangle.

What is Area?

Area is the amount of surface a flat shape covers.

Imagine the top of a table, the floor of a classroom, or the surface of a book. The amount of space these flat surfaces take up is their area. We measure area in square units, such as square centimetres (cm²) or square metres (m²).

To understand area, think about covering a surface with small, equal squares. The number of squares needed to cover the entire surface without any gaps or overlaps is the area.

Area of a Rectangle Using a Formula

A rectangle is a four-sided shape where opposite sides are equal in length and all angles are right angles (like the corner of a book).

Every rectangle has a length and a width (sometimes called breadth). The length is usually the longer side, and the width is the shorter side.

To find the area of a rectangle, you can multiply its length by its width. This gives you the number of square units that fit inside the rectangle.

The formula for the area of a rectangle is:

$$ \text{Area} = \text{Length} \times \text{Width} $$

Or, using symbols:

$$ A = L \times W $$

Remember that the unit for area will always be a square unit, such as square centimetres (cm²), square metres (m²), or square kilometres (km²).

Worked Examples: Calculating the Area of Rectangles

Example 1:

A rectangular table has a length of 120 cm and a width of 60 cm. Find the area of the table top.

Solution:

1. Identify the given values:
   Length (L) = 120 cm
   Width (W) = 60 cm
2. Write down the formula for the area of a rectangle:
   Area = L $\times$ W
3. Substitute the values into the formula and calculate:
   Area = 120 cm $\times$ 60 cm
   Area = 7200 cm²

The area of the table top is 7200 square centimetres.

Example 2:

A classroom floor is 9 metres long and 7 metres wide. What is the area of the classroom floor?

Solution:

1. Identify the given values:
   Length (L) = 9 m
   Width (W) = 7 m
2. Write down the formula:
   Area = L $\times$ W
3. Substitute and calculate:
   Area = 9 m $\times$ 7 m
   Area = 63 m²

The area of the classroom floor is 63 square metres.

Calculating the Area of Rectangular Farmland

Farmers often need to know the area of their land. This helps them decide how much seed to plant, how much fertiliser to use, or how many crops can grow in a certain space. Many farmlands are rectangular in shape.

To find the area of a rectangular farmland, we use the same formula: Length $\times$ Width.

Worked Examples: Area of Farmland

Example 1:

Mr. Audu has a rectangular farmland that is 50 metres long and 30 metres wide. What is the area of his farmland?

Solution:

1. Given:
   Length (L) = 50 m
   Width (W) = 30 m
2. Formula:
   Area = L $\times$ W
3. Calculation:
   Area = 50 m $\times$ 30 m
   Area = 1500 m²

The area of Mr. Audu’s farmland is 1500 square metres.

Example 2:

A community wants to clear a rectangular plot of land for a new garden. The plot is 25 metres long and 15 metres wide. What is the total area of the land for the garden?

Solution:

1. Given:
   Length (L) = 25 m
   Width (W) = 15 m
2. Formula:
   Area = L $\times$ W
3. Calculation:
   Area = 25 m $\times$ 15 m
   Area = 375 m²

The total area of the land for the garden is 375 square metres.

Quantitative Aptitude Problems Related to Area of Rectangle

Quantitative aptitude problems test your ability to understand and apply mathematical concepts to solve real-life situations. For the area of rectangles, these problems might involve finding a missing side, comparing areas, or solving word problems that require careful reading.

Worked Examples: Quantitative Aptitude Problems

Example 1:

A rectangular mat has an area of 48 square metres. If its length is 8 metres, what is its width?

Solution:

1. Given:
   Area (A) = 48 m²
   Length (L) = 8 m
2. We know the formula: Area = L $\times$ W
3. To find the width (W), we can rearrange the formula:
   W = Area $\div$ L
4. Substitute the values and calculate:
   W = 48 m² $\div$ 8 m
   W = 6 m

The width of the rectangular mat is 6 metres.

Example 2:

Two rectangular pieces of fabric are available. Fabric A is 10 cm long and 5 cm wide. Fabric B is 8 cm long and 7 cm wide. Which fabric has a larger area?

Solution:

1. Calculate the area of Fabric A:
   Area A = Length $\times$ Width
   Area A = 10 cm $\times$ 5 cm
   Area A = 50 cm²
2. Calculate the area of Fabric B:
   Area B = Length $\times$ Width
   Area B = 8 cm $\times$ 7 cm
   Area B = 56 cm²
3. Compare the areas:
   56 cm² (Fabric B) is greater than 50 cm² (Fabric A).

Fabric B has a larger area.

Example 3:

A painter needs to paint a rectangular wall that is 6 metres long and 4 metres high. If one can of paint covers 12 square metres, how many cans of paint will the painter need?

Solution:

1. First, find the area of the wall:
   Length (L) = 6 m
   Width (W) = 4 m
   Area of wall = L $\times$ W = 6 m $\times$ 4 m = 24 m²
2. Next, find out how many cans of paint are needed:
   Area covered by one can = 12 m²
   Number of cans = Total area $\div$ Area covered by one can
   Number of cans = 24 m² $\div$ 12 m²
   Number of cans = 2

The painter will need 2 cans of paint.