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150 LearnersLast updated on September 15, 2025
Area of Shapes
Area is the space inside the boundaries of a two-dimensional shape or surface. There are different formulas for finding the area of various shapes/figures. These are widely used in architecture and design. In this section, we will find the area of different shapes.
Area of Different Shapes Formula
Each shape has its own formula for calculating area. Here are a few key formulas:
1. Square: Area = side × side
2. Rectangle: Area = length × width
3. Triangle: Area = 1/2 × base × height
4. Circle: Area = π × radius²
The formulas are derived based on the properties of each shape. For instance, a square's area is calculated by squaring the length of its side, a rectangle's by multiplying its length and width, and a circle's by multiplying π (pi) with the square of its radius.
How to Find the Area of Shapes?
We can find the area of shapes using various methods depending on the shape:
Using Side Lengths: For squares and rectangles, use the lengths of the sides.
Using Base and Height: For triangles and parallelograms, use the base and height.
Using Radius: For circles, use the radius.
Let's discuss some examples:
1. Square: If the side length is 5 cm, the area is 5 × 5 = 25 cm².
2. Rectangle: With a length of 8 cm and width of 3 cm, the area is 8 × 3 = 24 cm².
3. Triangle: With a base of 6 cm and height of 4 cm, the area is 1/2 × 6 × 4 = 12 cm².
4. Circle: With a radius of 7 cm, the area is π × 7² = approximately 153.94 cm².
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Units of Area
We measure area in square units. The measurement depends on the system used:
In the metric system, the area is measured in square meters (m²), square centimeters (cm²), and square millimeters (mm²).
In the imperial system, the area is measured in square inches (in²), square feet (ft²), and square yards (yd²).
Special Cases or Variations for the Area of Shapes
Specific shapes have unique properties that affect how their area is calculated.
Consider these variations:
1. Circle: The formula uses π, a constant approximately equal to 3.14159.
2. Triangle: Besides base and height, you can also use Heron's formula when all sides are known.
3. Parallelogram: Similar to a rectangle, but height is the perpendicular distance from the base.
4. Trapezoid: Uses a different formula: Area = 1/2 × (baseโ + baseโ) × height.
Tips and Tricks for Area of Shapes
To ensure accuracy when calculating the area of shapes:
Common Mistakes and How to Avoid Them in Area of Shapes
It is common for mistakes to occur when finding the area of shapes. Here are some common mistakes and how to avoid them:
Mistake 1
Using incorrect formulas for different shapes
Ensure you use the correct formula for each shape.
For example, do not use the formula for a rectangle when calculating the area of a triangle.
Mistake 2
Mixing units of measurement
When calculating area, ensure all measurements are in the same unit.
Convert units when necessary to maintain consistency.
Mistake 3
Assuming all angles are right angles
Only certain shapes, like squares and rectangles, have right angles.
Be cautious with triangles and other polygons.
Mistake 4
Confusing radius and diameter in circles
Remember that the radius is half the length of the diameter.
Use the correct measurement in the formula for the area of a circle.
Mistake 5
Overlooking height in triangles and parallelograms
For triangles and parallelograms, ensure you use the perpendicular height, not a slant height or side length.
Area of Shapes Examples
Problem 1
A rectangular garden has a length of 10 m and a width of 5 m. What is the area?
The area is 50 m².
Explanation
The area of a rectangle is calculated as length × width.
Here, the length is 10 m, and the width is 5 m.
Therefore, the area = 10 × 5 = 50 m².
Problem 2
Find the area of a triangle with a base of 12 m and height of 9 m.
The area is 54 m².
Explanation
The area of a triangle is calculated as 1/2 × base × height.
Here, the base is 12 m, and the height is 9 m.
Therefore, the area = 1/2 × 12 × 9 = 54 m².
Problem 3
A circle has a radius of 3 cm. What is its area?
The area is approximately 28.27 cm².
Explanation
The area of a circle is calculated as π × radius².
Here, the radius is 3 cm.
Therefore, the area = π × 3² = π × 9 ≈ 28.27 cm².
Problem 4
If a square has a side length of 7 cm, what is its area?
The area is 49 cm².
Explanation
The area of a square is calculated as side × side.
Here, the side length is 7 cm.
Therefore, the area = 7 × 7 = 49 cm².
Problem 5
A parallelogram has a base of 8 m and height of 4 m. What is its area?
The area is 32 m².
Explanation
The area of a parallelogram is calculated as base × height.
Here, the base is 8 m, and the height is 4 m.
Therefore, the area = 8 × 4 = 32 m².
FAQs on Area of Shapes
1.Can the area of a shape be negative?
2.How do you find the area of a circle if only the diameter is given?
3.How to find the area of a triangle if only the side lengths are known?
4.How is the perimeter different from the area?
5.What is the significance of the area in real life?
Glossaries of Terms Related to Area of Shapes
- Area: The total space enclosed within a shape's boundaries, measured in square units.
- Perimeter: The total distance around the boundary of a shape.
- Radius: The distance from the center to the edge of a circle.
- Base: The side of a polygon used as a reference for calculating area or height.
- Height: The perpendicular distance from the base to the topmost point of a shape.
Seyed Ali Fathima S
About the Author
Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.
Fun Fact
: She has songs for each table which helps her to remember the tables
