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 Plane Figures


In mathematics, the term "plane figure" refers to any two-dimensional shape that lies on a flat surface. These shapes are characterized by their length and width, but they have no depth. Understanding how to calculate the area of plane figures is important not only for mathematical calculations but also for real-life applications involving space and capacity.

Understanding the region

The area of a shape is the space it occupies on a flat surface. Imagine you want to paint a wall or put a carpet on the floor - the area tells you how much material you need!

Mathematically, area is usually expressed in square units, such as square meters (m 2), square centimeters (cm 2), or square inches (in 2).

Area formula

The formula for calculating the area depends on the specific type of plane figure. Below are some common formulas for different shapes:

  • Rectangle: Area = length × width
  • Square: Area = side × side = side 2
  • Triangle: Area = 1/2 × base × height
  • Circle: Area = π × radius 2

Rectangle

Rectangles have four right angles. The area of a rectangle is found by multiplying the length by the width.

Example

Imagine a rectangle whose length is 8 cm and width is 5 cm. The area will be calculated as follows:

    Area = length × width = 8 cm × 5 cm = 40 cm 2
Length = 8 cm Width = 5 cm

Square

A square is a special rectangle whose all sides are of equal length. To calculate the area of a square, one has to find the square of the length of one of its sides.

Example

Consider a square whose each side is 4 cm. Its area is:

    Area = side × side = 4 cm × 4 cm = 16 cm 2
Side = 4 cm

Triangle

Triangles have three sides and three angles. To find the area of a triangle, we use a formula based on its base and height.

Example

If the base of a triangle is 10 cm and height is 6 cm, then its area is:

    Area = 1/2 × base × height = 1/2 × 10 cm × 6 cm = 30 cm 2
Base = 10 cm Height = 6 cm

Circle

Circles are round shapes. The area of a circle is calculated using the radius of the circle.

Example

The area of a circle of radius 3 cm is:

    Area = π × radius 2 = π × 3 cm × 3 cm = 28.27 cm 2
Radius = 3 cm

Irregular shape

For shapes that do not fit standard formulas, we can calculate the area by breaking them down into smaller, regular shapes, or by using grid paper to count perfect squares within the shape.

Example

Suppose we have an L-shape made up of two rectangles: one 4 cm by 3 cm and the other 2 cm by 3 cm. We can divide the L-shape into these two rectangles, calculate the area of each, and add them together.

    Area of first rectangle = 4 cm × 3 cm = 12 cm 2 Area of second rectangle = 2 cm × 3 cm = 6 cm 2 Total area = 12 cm 2 + 6 cm 2 = 18 cm 2
4 cm × 3 cm 2 cm × 3 cm

Importance of units

In all the calculations above, pay attention to how the area is expressed in square units. It is important to convert the measurements into the same units before applying them to any formulas.

For example, if you have the dimensions of a rectangle 200 cm by 1.5 m, convert them to centimeters or meters:

    Area = 200 cm × 150 cm = 30,000 cm 2

Conversion tips

  • 1 meter = 100 centimeters
  • 1 meter = 1000 millimeters
  • 1 kilometer = 1000 meters

Uses of area in real life

Understanding how area is calculated is valuable in a variety of real-world scenarios:

  • Home improvement: When painting walls, buying carpet, or laying tiles, calculating the area ensures you buy the right amount of materials.
  • Agriculture: Farmers assess the area of their fields to determine how much seed they need to plant.
  • Architecture and engineering: Engineers and architects use area calculations in design and construction plans.

Practice problems

Test your understanding with these practice problems:

  1. The dimensions of a rectangle are 14 cm by 9 cm. Find its area.
    2.       Area = length × width = 14 cm × 9 cm = 126 cm 2
  2. The length of the side of a square is 7 cm. What is its area?
    3.       Area = side × side = 7 cm × 7 cm = 49 cm 2
  3. The base of a triangle is 12 cm and the height is 8 cm. Find its area.
    4.       Area = 1/2 × base × height = 1/2 × 12 cm × 8 cm = 48 cm 2
  4. The radius of a circle is 5 cm. Find the area.
    5.       Area = π × radius 2 = π × 5 cm × 5 cm ≈ 78.54 cm 2

Conclusion

Mastering the concept of area is vital in practical scenarios in math and everyday life. Remember to use the correct formula based on the shape, make sure the units are consistent, and confidently apply your knowledge to real-world problems.


Grade 7 → 5.1.2


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Perimeter of Plane Figures
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Area of Plane Figures

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