Grade 6
  1. Number System  1.1. Whole Numbers  1.1.1. Place Value and Face Value  1.1.2. Comparing and Ordering Numbers  1.1.3. Rounding Numbers  1.1.4. Properties of Whole Numbers (Associative, Commutative, Distributive)  1.2. Integers  1.2.1. Introduction to Integers  1.2.2. Addition and Subtraction of Integers  1.2.3. Multiplication and Division of Integers  1.2.4. Properties of Integer Operations  1.3. Fractions  1.3.1. Types of Fractions  1.3.2. Equivalent Fractions  1.3.3. Simplification of Fractions  1.3.4. Addition and Subtraction of Fractions  1.3.5. Multiplication and Division of Fractions  1.3.6. Comparing and Ordering Fractions  1.4. Decimals  1.4.1. Understanding Decimals  1.4.2. Conversion between Fractions and Decimals  1.4.3. Addition and Subtraction of Decimals  1.4.4. Multiplication and Division of Decimals  1.4.5. Comparing and Ordering Decimals
  2. Algebra  2.1. Basics of Algebra  2.1.1. Variables and Constants  2.1.2. Expressions and Equations  2.1.3. Algebraic Terms and Coefficients  2.2. Solving Simple Equations  2.2.1. Balancing Equations  2.2.2. Solving One-Step Equations  2.2.3. Solving Two-Step Equations  2.3. Patterns and Sequences  2.3.1. Identifying Patterns  2.3.2. Arithmetic Sequences
  3. Ratio and Proportion  3.1. Ratios  3.1.1. Understanding Ratios  3.1.2. Equivalent Ratios  3.1.3. Simplifying Ratios  3.2. Proportion  3.2.1. Introduction to Proportion  3.2.2. Direct and Inverse Proportions  3.3. Percentages  3.3.1. Converting Ratios to Percentages  3.3.2. Percentage Increase and Decrease  3.3.3. Discount and Profit Calculations  3.3.4. Simple Interest Calculations in Percentages in Ratio and Proportion
  4. Geometry  4.1. Basic Geometric Shapes  4.1.1. Points, Lines, and Angles  4.1.2. Types of Angles  4.1.3. Intersecting and Parallel Lines  4.2. Triangles  4.2.1. Types of Triangles  4.2.2. Properties of Triangles  4.2.3. Sum of Angles in a Triangle  4.2.4. Congruence of Triangles  4.3. Quadrilaterals  4.3.1. Types of Quadrilaterals  4.3.2. Properties of Quadrilaterals  4.4. Circles  4.4.1. Radius and Diameter  4.4.2. Circumference and Area  4.4.3. Arcs and Chords  4.4.4. Sector and Segment
  5. Mensuration  5.1. Perimeter  5.1.1. Perimeter of Simple Shapes  5.2. Area  5.2.1. Area of Rectangles and Squares  5.2.2. Area of Triangles and Parallelograms  5.2.3. Area of Composite Figures  5.2.4. Area of Trapezium  5.3. Volume  5.3.1. Volume of Cubes and Cuboids  5.3.2. Volume of Cylinders  5.3.3. Volume of Cones  5.3.4. Surface Area of Simple Solids
  6. Data Handling  6.1. Introduction to Data  6.1.1. Types of Data  6.1.2. Organizing Data  6.1.3. Frequency Distribution  6.2. Graphs and Charts  6.2.1. Bar Graphs  6.2.2. Line Graphs  6.2.3. Pictographs  6.2.4. Pie Charts  6.3. Mean, Median, and Mode  6.3.1. Calculating Mean  6.3.2. Finding Median  6.3.3. Identifying Mode  6.3.4. Range of Data in Mean, Median, and Mode
  7. Probability  7.1. Basics of Probability  7.1.1. Understanding Probability  7.1.2. Probability of Simple Events  7.1.3. Experimental and Theoretical Probability
  8. Practical Geometry  8.1. Construction of Shapes  8.1.1. Constructing Triangles  8.1.2. Constructing Quadrilaterals  8.1.3. Constructing Circles and Arcs  8.2. Symmetry  8.2.1. Line of Symmetry  8.2.2. Rotational Symmetry  8.2.3. Translational Symmetry

Grade 6 → Mensuration → Area ↓


Area of Triangles and Parallelograms


In math, measuring area is important to understand how much space is available inside a shape. This lesson will help you understand how to calculate the area of two common shapes: a triangle and a parallelogram. Let's learn how to find the area of these shapes, step by step, with lots of examples.

Finding the area of a triangle

A triangle is a simple figure that has three sides and three angles. To find the area of a triangle, you need to know the base and the height. The formula to calculate the area is:

Area of Triangle = (base × height) / 2

Here, the base is any one side of the triangle, and the height is the perpendicular distance from the base to the opposite vertex. Let's look at an example of finding the area of a triangle.

Example 1: Simple triangle

Consider a triangle with a base of 8 units and a height of 5 units. Using the formula, we can find the area.

Area = (8 × 5) / 2 = 40 / 2 = 20 square units

The area of the triangle is 20 square units.

Here is a visual representation:

Base = 8 height = 5

Let’s look at some more examples!

Example 2: Triangle with different base and height

Imagine a triangle whose base is 10 units and height is 6 units. What will be its area?

Area = (10 × 6) / 2 = 60 / 2 = 30 square units

Therefore, the area of this triangle is 30 square units.

Example 3: Triangular area

Suppose you have a triangular field with a long base of 15 m and a height of 10 m. Calculate the area to find out how much space you have.

Area = (15 × 10) / 2 = 150 / 2 = 75 square meters

The entire ground is spread over an area of 75 square meters.

Finding the area of a parallelogram

A parallelogram is a four-sided shape in which each pair of opposite sides is parallel. To calculate the area, you need to know the base and height, just like a triangle. The formula for the area of a parallelogram is:

Area of Parallelogram = base × height

In a parallelogram, the base can be any side, and the height is the perpendicular distance between the chosen base and the opposite side. Let us explain how to find the area through examples.

Example 1: Simple parallelogram

Suppose the base of a parallelogram is 10 units and the height is 5 units. We find the area using the formula.

Area = 10 × 5 = 50 square units

The area of this parallelogram is 50 square units.

Here is a visual representation:

Base = 10 height = 5

Now, let's work on some more examples for better understanding.

Example 2: Garden plan

Imagine a garden that is in the shape of a parallelogram with a base of 14 units and a height of 8 units. What is the area of the garden?

Area = 14 × 8 = 112 square units

The area of the garden is 112 square units.

Example 3: Large parallelogram area

Now consider a ground with a base of 20 m and a height of 12 m. We need the area to know how much space it occupies.

Area = 20 × 12 = 240 square meters

Thus, the area of the field is 240 square metres.

Comparing triangles to parallelograms

Looking at both triangles and parallelograms, we see similarities and differences in finding their areas. Both require base and height for calculation. However, the main difference is that for triangles, we divide by 2, while for parallelograms, we do not. Why is that so? Let's understand why.

If you take a parallelogram, you can divide it into two equal triangles. This is why the formula for finding the area of a triangle involves dividing by 2. Conceptually, two equal triangles put together will form a shape like a parallelogram.

To visualize:

Base Height Triangle 1 Triangle 2

So whenever we talk about the area of these figures, remember that it means understanding how much plane surface they cover with the given dimensions.

Practical application and problem solving

Knowing how to calculate the area of triangles and parallelograms is very useful in various real-life scenarios. For example, architects use these calculations to design buildings, engineers to plan bridges, and even farmers to know how much land they can use for crops.

Let's try to solve practical problems using these concepts:

Problem 1: Area of a triangular park

You are tasked with designing a triangular park whose sides are 30 meters, and the height from the chosen base is 24 meters. Find out how much space you are working with by calculating the area.

Area = (30 × 24) / 2 = 720 / 2 = 360 square meters

Therefore, the triangular park covers an area of 360 square metres.

Problem 2: Parallelogram land plot

Suppose you have a plot in the shape of a parallelogram with a base of 50 m and a height from this base of 25 m. Calculate the area to determine the shape of the plot.

Area = 50 × 25 = 1250 square meters

The area of your plot is 1,250 square metres.

Conclusion

Learning how to find the areas of triangles and parallelograms requires the use of simple mathematical formulas. By mastering these, we can easily calculate spaces for various practical needs. It is important to identify the base and perpendicular height in any context to use these formulas effectively. Practice with various examples, and you will be calculating area easily in no time.


Grade 6 → 5.2.2


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Area of Rectangles and Squares
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Area of Triangles and Parallelograms

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