Grade 7
  1. Number System  1.1. Integers  1.1.1. Properties of Integers  1.1.2. Operations on Integers  1.1.3. Additive and Multiplicative Inverses  1.1.4. Applications of Integers  1.2. Rational Numbers  1.2.1. Definition of Rational Numbers  1.2.2. Properties of Rational Numbers  1.2.3. Operations on Rational Numbers  1.2.4. Standard Form of Rational Numbers  1.3. Decimals  1.3.1. Operations on Decimals  1.3.2. Converting Between Fractions and Decimals  1.4. Powers and Exponents  1.4.1. Laws of Exponents  1.4.2. Simplifying Expressions with Exponents  1.4.3. Scientific Notation  1.5. Roots  1.5.1. Square Roots  1.5.2. Cube Roots
  2. Algebra  2.1. Expressions  2.1.1. Algebraic Expressions  2.1.2. Simplifying Expressions  2.1.3. Evaluating Expressions  2.2. Linear Equations  2.2.1. Solving Simple Equations  2.2.2. Applications of Linear Equations  2.3. Algebraic Identities  2.3.1. Expanding Using Identities  2.3.2. Simplifying Using Identities
  3. Ratio and Proportion  3.1. Ratios  3.1.1. Understanding Ratios  3.1.2. Simplifying Ratios  3.1.3. Equivalent Ratios  3.2. Proportion  3.2.1. Concept of Proportion  3.2.2. Direct Proportion  3.2.3. Inverse Proportion  3.3. Unitary Method  3.3.1. Solving Problems Using the Unitary Method
  4. Geometry  4.1. Lines and Angles  4.1.1. Types of Angles  4.1.2. Pairs of Angles  4.1.3. Properties of Parallel Lines and a Transversal  4.1.4. Angle Bisectors  4.2. Triangles  4.2.1. Types of Triangles  4.2.2. Angle Sum Property  4.2.3. Exterior Angle Property  4.2.4. Pythagoras Theorem  4.3. Congruence of Triangles  4.3.1. Criteria for Congruence  4.3.2. Applications of Congruence  4.4. Quadrilaterals  4.4.1. Types of Quadrilaterals  4.4.2. Properties of Parallelograms  4.4.3. Special Quadrilaterals  4.4.4. Properties of Rectangles and Rhombuses
  5. Mensuration  5.1. Perimeter and Area  5.1.1. Perimeter of Plane Figures  5.1.2. Area of Plane Figures  5.1.3. Area of a Trapezium  5.1.4. Area of a Parallelogram  5.1.5. Area of a Circle  5.1.6. Area of Composite Figures  5.2. Surface Area and Volume  5.2.1. Cubes and Cuboids  5.2.2. Surface Area of Cylinders  5.2.3. Volume of Prisms and Cylinders  5.2.4. Volume and Surface Area of Cones
  6. Data Handling  6.1. Data Collection  6.1.1. Organizing Data  6.1.2. Frequency Distribution  6.2. Graphical Representation of Data  6.2.1. Bar Graphs  6.2.2. Double Bar Graphs  6.2.3. Pie Charts  6.2.4. Histograms  6.2.5. Line Graphs  6.3. Probability  6.3.1. Simple Events  6.3.2. Experimental Probability  6.3.3. Theoretical Probability
  7. Practical Geometry  7.1. Construction of Triangles  7.1.1. Constructing Triangles Given Side Lengths  7.1.2. Constructing Triangles Given Side and Angle  7.1.3. Constructing Right-Angled Triangles  7.2. Construction of Quadrilaterals  7.2.1. Quadrilaterals Given Side Lengths and Angles  7.2.2. Constructing Parallelograms and Rectangles

Grade 7 → Mensuration → Perimeter and Area ↓


Area of a Trapezium


In this topic, we will dive into the fascinating world of trapezoids and find out how to find the area of a trapezoid. It is an essential part of measurement in mathematics, which deals with measuring the size, area, and volume of various shapes and figures. By the end of this explanation, you should be able to easily understand and calculate the area of a trapezoid.

What is a trapezoid?

A trapezoid is a four-sided polygon, also called a quadrilateral, with at least one pair of parallel sides. These parallel sides are called the "bases" of the trapezoid. The other two sides are called the "legs."

Here is a simple representation of a trapezoid:

A ___________ B
/          
/            
C ------------- D

In this diagram, AB and CD are the parallel sides or bases of the trapezoid. AC and BD are the non-parallel sides.

Understanding the components of a trapezoid

To effectively calculate the area of a trapezoid, it is important to understand some basic terminology and geometry:

  • Bases: These are the parallel sides of the trapezoid. In our example above, AB and CD are the bases.
  • Height (h): This is the perpendicular distance between the bases. It is often represented by the letter h.
  • Legs: These are the non-parallel sides of the trapezoid. These are the sides that are not parallel to each other and meet at the bases.

In the trapezoid shown above, the height (h) is not shown. The height is always perpendicular to the bases.

Formula for the area of a trapezoid

The formula for finding the area of a trapezoid is based on two bases and the height. It is given by the following equation:

Area = (1/2) × (Base1 + Base2) × Height

In this formula:

  • Base1 and Base2 are the lengths of the parallel sides (bases).
  • Height is the perpendicular distance between these bases.

Example 1: Finding the area of a trapezoid

Let's consider a trapezoid whose Base1 is equal to 8 units, Base2 is equal to 5 units, and Height (h) is equal to 4 units. Using the formula for the area of a trapezoid:

Area = (1/2) × (8 + 5) × 4 = (1/2) × 13 × 4 = 26 square units

Drawing of trapezoid and its area

Sometimes visualizing a trapezoid can help you understand how the area is determined. Here is a presentation to illustrate this concept:

Base 1 Base2 Height

By looking at the trapezoid and identifying each of its components, such as the base and height, you can easily plug the corresponding values into the formula and calculate the area.

More examples and applications

Example 2: A real-world application

Imagine that you are designing a garden, and you want to create a flower bed in the shape of a trapezoid. The top length of the bed is 5 m, the bottom length is 7 m, and the distance between these sides (height) is 1 m. The distance between the plants is 3 m. To find the area for planting flowers, calculate as follows:

Area = (1/2) × (5 + 7) × 3 = (1/2) × 12 × 3 = 18 square meters

This means you have 18 square meters of space available for planting.

Example 3: Calculating area with large numbers

Consider a trapezoid whose Base1 is equal to 14 units, Base2 is equal to 18 units, and Height (h) is equal to 10 units.

Area = (1/2) × (14 + 18) × 10 = (1/2) × 32 × 10 = 160 square units

The area of this trapezoid is 160 square units.

Test your understanding

Here are some practice problems to help strengthen your understanding:

  1. The lengths of the bases of a trapezium are 6 cm and 10 cm and the height is 4 cm. What is its area?
  2. Find the area of a trapezium with Base1 = 12 units, Base2 = 9 units, and Height = 5 units.
  3. Find the area of a trapezium, where Base1 20 m, Base2 is 15 m and height is 8 m.

Conclusion

By understanding the properties and formula of a trapezoid, we can find its area, which is an important skill in mathematics and various real-world applications. Measuring shapes like trapezoids is a great way to explore space within structures, gardens, construction, and much more. Practicing with a variety of examples helps to solidify this knowledge, making it easier to tackle a wide range of mathematical problems.

We hope this detailed explanation has given you a better idea of how to find the area of a trapezoid. Keep practicing, and you'll be an expert in no time!


Grade 7 → 5.1.3


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Area of Plane Figures
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Area of a Trapezium

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