Area: Definition, Formulas & Sample Problems

Learning the properties of different shapes and applying the formulas to calculate area helps students build a solid foundation for various advanced math concepts. Calculating the area of shapes is one of the necessary math skills applied in our day-to-day life to evaluate the cost of flooring, painting, land area, and so on. With the simple examples and exercises given on this page, kids will be able to grasp the concepts of area and its application easily.

Table of Contents

• Definition of Area
• How to Calculate the Area of Shapes?
• Area Formulas and Examples
• Application of Area Concepts
• Sample Problems-on-Area
• Frequently Asked Questions on Area

Definition of Area

Area is the measure of the space enclosed within a two-dimensional surface or shape. It depicts the amount of surface a shape covers and is typically measured in square units like square centimetres (cm²), square meters (m²), or square inches (in²). For example: A rectangle with a length of 5 cm and a width of 4 cm has an area of 20 cm².

How to Calculate the Area of Shapes?

To calculate the area of various 2D and 3D shapes, we use different formulas depending on the type of shape. There is a different area formula for each geometric figure, such as rectangles, triangles, circles, etc. In general, the process of finding the area of a shape involves the following:

1. Identifying the type of shape: By studying all concepts related to the area of 2D and 3D shapes, we can solve many real-world problems easily.

2. Use the correct area formula for the shape.

3. Substitute the values in the formula and solve it to get the correct answer.

 

Area Formulas and Examples

 

Application of Area Concepts

The concept of finding the area of shapes is applied in various fields, including architecture, design, construction, agriculture, math and physics. Some of the major applications of the area concept are explained below:

 

• Construction & Architecture: Engineers use various formulas to measure floor area, land area, room sizes, and flooring while constructing and designing houses as well as roads, bridges, etc.

 

• Interior Design: The concept of area is applied in calculating the quantity of paint, length of wallpaper, carpeting area, number of tiles required, etc. to design the spaces.

 

• Agriculture: Land area estimation also helps in determining the field size for planting seeds or channeling irrigation pipes, etc.

 

• Mathematics & Science: Mathematicians and scientists use various concepts of area in solving geometry, physics, and engineering problems.

 

• Everyday Life: We calculate area in our daily life from packing gifts and sewing fabrics to cutting materials for creating art.

Sample Problems on Area

Problem 1:

Find the area of a triangle with a base of 10 cm and height of 6 cm.

Solution:

Area = ½ × base × height = ½ × 10 × 6 = 30 cm²

 

Problem 2:

A rectangle has a length of 12 m and a width of 5 m. What is its area?

Solution:

Area = length × width = 12 × 5 = 60 m²

 

Problem 3:

Calculate the area of a circular disc with a radius of 7 cm.

Solution:

Area = π × r² = 22/7 × 7² ≈ 154 cm²

Summary
Understanding area helps students build a strong foundation for problem-solving skills. Whether you're calculating the size of a carpet or working on a math test, knowing how to calculate area and use formulas effectively is a must.

Frequently Asked Questions on Area

1: What is the unit of area?

Answer: The area is measured in square units, such as square centimeters (cm²), square meters (m²), square feet (ft²), or square inches (in²).

2: Can the area be negative?

Answer: No. Area cannot be negative. It is the measure of space that can only be a positive value.

3: Explain the difference between area and perimeter.

Answer: The area of a shape is the measure of the surface enclosed within a shape, while perimeter is the measure of the distance around the shape.

4: Is the area concept used in 3D shapes?

Answer: Yes, but in 3D shapes, we often calculate surface area (total area covering all faces). 

5. What is the formula for area?

Answer: The formula of area depends on the shape. There are different formulas used for various 2D and 3D shapes.

6. What is the area of a rectangle?

Answer: The formula to calculate the area of a rectangle is the product of its length and breadth. I.e., A = L x B

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