Area

In mathematics, area is a way of measuring the size of a surface. It tells us how much space is inside a shape. We use area to figure out how much carpet is needed to cover a floor, how many tiles are needed to cover a wall, or how much paint is needed to paint a wall.

What is the area?

Area is the amount of space inside a two-dimensional shape. The shape can be any flat object such as a square, rectangle, triangle, circle, etc. We measure area in square units, such as square meters (m²), square centimeters (cm²), or square inches (in²). This means that when we calculate area, we think about how many squares of a unit size can fit inside the shape.

The basic concept of the field

Think of the cover of a book. If you want to wrap it with paper without any gaps or overlaps, you need to know the area of the cover. Similarly, a farmer needs to know the area of his field to know how many seeds are needed to plant a crop.

Area of a rectangle

To find the area of a rectangle, multiply its length by its width. Imagine you have a rectangle that is 4 units long and 3 units wide. How do we find its area?

The formula for finding the area of a rectangle is:

Area = Length × Width

Example

If the length of a rectangle is 4 and the width is 3, then the area will be calculated as:

Area = 4 × 3 = 12 square units

The above figure shows a rectangle with 4 units length and 3 units width, which forms an area of 12 square units, because 4 times 3 equals 12.

Area of a square

A square is a special type of rectangle in which all sides are equal. To find its area, you just have to multiply the side by itself because the length and width are equal.

The formula for finding the area of a square is:

Area = Side × Side

Example

If one side of a square is 5 units long, then its area is:

Area = 5 × 5 = 25 square units

The above diagram shows a square with each side being 5 units, making the area of the square 25 square units.

Area of a triangle

Triangles are a little tricky because they have three sides. We use a different formula to find the area. This formula is:

Area = (Base × Height) / 2

Example

If the base of a triangle is 6 units and the height is 4 units, then its area is:

Area = (6 × 4) / 2 = 12 square units

In the above figure we see a triangle whose base is 6 units and height is 4 units.

Area of a circle

A circle is a figure with a radius. The radius is the distance from the center of the circle to its edge. To find the area of a circle, we use the formula:

Area = π × Radius × Radius

Here, π (pi) is a special number, which is approximately 3.14.

Example

If the radius of a circle is 3 units, then its area will be:

Area = 3.14 × 3 × 3 = 28.26 square units

The above figure shows a circle with radius 3 units.

Uses of area in real life

Knowing how to calculate area is helpful in many practical situations, such as:

• When building a house, plan how much space you will have.
• When planting a garden, it is important to know how many plants will fit.
• When purchasing flooring, check how many tiles will be needed.
• For even cooking, layer ingredients in a container to ensure even coverage.

Practice problems

1. What is the area of a rectangle with 7 units length and 3 units width?

Solution:

Area = 7 × 3 = 21 square units

2. Each side of a square garden is 10 units. What is its area?

Solution:

Area = 10 × 10 = 100 square units

3. Find the area of a triangle with a base of 8 units and a height of 5 units.

Solution:

Area = (8 × 5) / 2 = 20 square units

4. The radius of a circle is 4 units. Find its area.

Solution:

Area = 3.14 × 4 × 4 = 50.24 square units

Conclusion

Understanding area is essential because it applies to both daily activities and a variety of academic subjects. By knowing how to calculate the area of different shapes, such as rectangles, squares, triangles, and circles, you can solve a variety of practical problems. Practicing calculations helps you remember the formulas and apply them correctly.

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