Area of Rectangles

When you look around you, many things are rectangular in shape such as books, doors or computer screens. In math, understanding the area of these rectangles helps us measure how much space they take up. Area tells us how many square units can fit inside that shape.

The basic idea of a rectangle is simple. It is a four-sided shape with opposite sides being equal and every angle being a right angle, meaning that it measures 90 degrees. To understand area, we first learn how the length of the sides of a rectangle relates to the total space it takes up on a flat surface.

What is the area of a rectangle?

The area of a rectangle is the total space covered by the rectangle on a flat surface. We measure this space in square units (such as square meters, square centimeters, etc.). To find the area of a rectangle, you multiply the length of one side by the length of the side across from it.

The formula for area is:

Area = Length × Width

Here, "length" is the length of the rectangle, while "width" is the width of the rectangle. Multiplying these two measurements gives you the area.

Let's look at a visual example to understand this concept:

In this simple example, the top and bottom sides of the rectangle are the length, and the sides are the width. Using the formula, the area is obtained by multiplying the length by the width.

Example problems

Example 1

Suppose we have a rectangle with 12 units length and 4 units width. This is how we find the area:

Area = 12 × 4 = 48 square units

This means that 48 square units will be needed to cover the entire surface of the rectangle.

Example 2

Suppose we have another rectangle but this time it has a length of 7 units and a width of 3 units. We find the area like this:

Area = 7 × 3 = 21 square units

Here, the rectangle covers 21 square unit space.

Visualization of the area with small squares

Sometimes, it is helpful to imagine a rectangle as a set of smaller squares. This visualization can make it easier to understand how area works.

Suppose we have a rectangle that measures 4 units by 3 units. If we fill this rectangle with squares that are 1 unit by 1 unit, it will look like this:

This shows how the 12 smaller squares fit perfectly into the rectangle, and shows that the total area of the rectangle is 12 square units.

Real life applications of rectangle area

Knowing how to find the area of a rectangle is very useful in everyday life. Here are some scenarios where calculating the area is helpful:

• Painting a wall: If you need to paint a rectangular wall, you need to calculate its area to figure out how much paint is needed.
• Buying carpet: When carpeting a room, finding out the area of the room can help you determine how much carpet you will need to purchase.
• Gardening: If you're planting flowers in a rectangular area, knowing the area will help you plan how much space you have to plant.

Understanding rectangles and their areas makes these types of tasks easier to perform.

Practice problems

Below are some practice problems so you can test your understanding. Try to solve them using the formula we learned.

1. A rectangle is 10 units long and 5 units wide. What is its area?
2. If the measurement of a rectangle is 8 units by 3 units, how many square units is its area?
3. Find the area of a rectangle whose length is 9 units and width is 6 units.
4. How big is the area of a rectangle that is 15 units by 7 units?

Conclusion

The area of a rectangle is a fundamental concept in geometry that plays an important role in both mathematics and real-world situations. By learning how to calculate area using length and width, you can apply this skill in countless scenarios. Practicing with visual and numerical examples strengthens understanding and builds confidence in solving area problems.

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