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 Composite Figures


Compound shapes are shapes that are made up of two or more simple geometric shapes. These can include rectangles, squares, triangles, circles, or other polygons. The challenge is to find the area of these shapes because they are not standard geometric shapes like we usually learn individually. However, by breaking them down into their simpler components, we can find their total area.

Remember, area is the amount of space inside a figure or shape. When finding the area of composite shapes, our task is to add the areas of the simple shapes that make up the composite figure. Let's see how we can do this step-by-step, and use examples to solidify our understanding.

Methods for finding the area of composite figures

To find the area of composite shapes we can generally follow these steps:

  1. Identify all the simple shapes that make up a compound figure. These shapes can be rectangles, triangles, circles, and other polygons.
  2. Calculate the area of each simple shape using their respective formulas.
  3. Sum the areas of all the simple shapes to find the total area of the composite figure.

Formulas for simple geometric shapes

Let's review formulas for calculating the area of some simple shapes:

  • Rectangle: Area = length × width
  • Square: Area = side × side = side 2
  • Triangle: Area = (base × height) / 2
  • Circle: Area = π × radius 2, where π (pi) is approximately 3.14

Visual example 1: Shape of a house

Consider a house-shaped figure that is a combination of a rectangle and a triangle. Here is a diagram of that figure:

rectangleTriangle

To find the total area of a house-shaped composite figure, we would do:

  1. Find the area of the rectangle. Let the portion of the rectangle be 100 units long and 70 units wide.
  2. Find the area of the triangle. Let the base of the triangle be equal to the width of the rectangle (100 units) and its height is 60 units.
  3. Add the two areas to find the total area of the house.

Calculation:

Area of rectangle = 100 * 70 = 7000 square units Area of triangle = (1/2) * 100 * 60 = 3000 square units Total area = Area of rectangle + Area of triangle = 7000 + 3000 = 10000 square units

Visual example 2: An L-shaped figure

Imagine a compound figure that looks like the letter "L". It can be seen as a combination of two rectangles. Below is a diagram showing this figure:

Verse 1Verse 2

For this L-shaped compound figure:

  1. Identify the two rectangles that form an L shape.
  2. Calculate the area of each rectangle separately.
  3. Add their areas to get the total area.

Suppose rectangle 1 is 100 units long and 40 units wide, and rectangle 2 is 40 units long and 70 units wide.

Area of Rectangle 1 = 100 * 40 = 4000 square units Area of Rectangle 2 = 40 * 70 = 2800 square units Total area = Area of Rectangle 1 + Area of Rectangle 2 = 4000 + 2800 = 6800 square units

Lesson example 1: Irregular shape area

Let us consider a practical example involving a garden. A garden has a rectangular portion with dimensions of 8 m by 6 m, and an adjacent triangular flower bed that is on one side of the rectangle. The base of the triangle is 8 m and its height is 3 m.

To find the area of the total garden:

  1. Find the area of the rectangular part of the garden using the formula: Area = length × width.
  2. Find the area of a triangular flower bed using the formula: Area = (base × height) / 2.
  3. Add these areas to find the total area of the garden.
Area of rectangle = 8 * 6 = 48 square meters Area of triangle = (1/2) * 8 * 3 = 12 square meters Total garden area = Area of rectangle + Area of triangle = 48 + 12 = 60 square meters

Lesson example 2: Mixed shape playground

Consider a playground with a square sandbox with a side of 5 m, adjacent to a semicircular swing area. The diameter of the semicircle is 10 m.

For the playground:

  1. Find the area of a square sandbox using the square formula: Area = side 2
  2. Calculate the area of a semicircular swing. First, find the area of a full circle using Area = π × radius 2, then divide it by 2, since it's a semicircle.
  3. Add the two areas to find the total area of the playing field.
Area of square = 5 * 5 = 25 square meters Radius of circle = 10 / 2 = 5 meters Area of full circle = π * 5 2 = 78.5 square meters (using π ≈ 3.14) Area of half-circle = 78.5 / 2 = 39.25 square meters Total playground area = Area of square + Area of half-circle = 25 + 39.25 = 64.25 square meters

Conclusion

Finding the area of compound shapes may seem tricky at first, but by breaking them down into simpler, familiar shapes, the process becomes much easier. Always start by identifying and isolating simple shapes, applying their area formulas, and adding the areas together.

Importantly, this process encourages analytical thinking by requiring you to visualize complex shapes and break them down into manageable parts. This skill is useful not only in math, but also in problem-solving scenarios you encounter in everyday life.

Practice with as many different shapes and configurations as possible to become proficient at calculating the area of compound shapes. As you progress, challenge yourself with more complex shapes and even try to create some compound shapes to test your skills.


Grade 7 → 5.1.6


U
username
0%
completed in Grade 7

← Prev (5.1.5)
Area of a Circle
Next (5.2) →
Surface Area and Volume

Comments 



Area of Composite Figures

https://www.buddymath.com/g7/5.1.6?bmal=en