Learning Objectives:

Pupils should be able to:

• Explain the concept of perimeter
• Find the perimeter of regular and irregular shapes
• Solve the perimeter of a circle
• Apply the concept of perimeter in solving problems and solve them

Learning Activities

• Pupils in pairs are asked to cut a polygon with measured shapes. They put the polygon together and ask pupils to discuss. After cutting out, they measure the total length around the shape being created.
• Pupils in small groups use tape to measure to measure the perimeter of the desks in the class.
• Pupils in small groups, wrap thread of string firmly around can top (circular pieces) to tie any knots as the string comes back to the starting point. Ask pupils to measure the length of string that was used to obtain the perimeter of form a polygon that can help to measure the line. This is the perimeter of the circle.

Embedded Core Skills

• Critical thinking and problem solving skills
• Communication and Collaboration
• Students leadership skills and Personal Development

Learning Resources

• Rules
• Terminal all perimeters of shapes
• Cardboard cut out of different shapes
• Textbooks and Workbook with polygon interest, discussed, and circumference formulas and examples

Content

Perimeter of Regular Shapes

Perimeter is the distance around the outside of a two-dimensional shape. It is a measure of the length that defines the outline of a shape. If the perimeter of a shape is the sum of all the sides in basic mathematics, specifically in geometry, to describe the size of a shape or the distance around it.

The perimeter of a rectangle is the distance around the outside of the rectangle. To find the perimeter, you add up the lengths of all four sides. For example, if the length of each side of a square is 5 units, then the perimeter would be 5 + 5 + 5 + 5 = 20 units.

The perimeter of a triangle is the distance around the outside of the triangle. To find the perimeter, you add up the lengths of all three sides. For example, if the length of a rectangle is 6 units and the width is 4 units, the perimeter would be 6 + 4 + 6 + 4 = 20 units.

The perimeter of a rectangle is the distance around the outside of the rectangle. To find the perimeter, you add up the lengths of all three sides. For example, if the length of the three sides of a triangle are 5 units, 7 units, and 8 units, the perimeter would be 5 + 7 + 8 = 20 units.

Formulas:

• Triangle C = the distance the circumference; it is increment (approximately 3.14) and r is the radius of the circle. For circles, the perimeter is called the “circumference” and the formula is C = 2πr, where π (pi) is a mathematical constant approximately equal to 3.14159.

The perimeter of a rectangle is the distance around the outside of the rectangle. To find the perimeter of a rectangle, we use the formula P = 2l + 2w or P = 2(l + w), where l is the length of the rectangle and w is the width; the perimeter would be 2 × 6 + 2 × 4 = 20 units.

The perimeter of a rectangle is the distance around the outside of the rectangle. To find the perimeter of a quadrilateral, you add up the lengths of all four sides. For example, of each side of a quadrilateral. To find the perimeter of a quadrilateral, you add up the lengths of all four sides; the perimeter would be 5+5+5+4+4 = 49 units.

Tip and the width is 5 units, the perimeter would be 5 + 6 + 5 + 6 = 20 units.

The perimeter of a square is the distance around the outside of the square. To find the perimeter of a square, you can multiply the length of one side by 4. For example, if each side of a square is 8 units, the perimeter would be 4 × 8 = 24 units.

The perimeter of a pentagon is the distance around the outside of the pentagon. To find the perimeter of a pentagon, you add up the lengths of all five sides. For example, if the length of the five sides of a pentagon is 10 units, because each side has equal circumference, the perimeter would be 10 + 10 + 10 + 10 + 10 = 50 units.

The perimeter of an irregular shape can be found by measuring the length of each side and then adding them together. This can be done by using a ruler or measuring tape. For example, if the sides are 8 units, 10 units, 6 units, and 12 units, the perimeter would be 8 + 10 + 6 + 12 = 36 units.

The perimeter of a regular plane shape is the distance around the outside of the shape. The formula for finding the perimeter depends on the type of shape. Here are some common formulas for regular shapes:

Examples: The perimeter of a triangle with sides of length 5 cm, 7 cm, and 8 cm. The lengths of all four sides: The perimeter is the distance around a shape. Let me explain using some examples:

5 cm + 7 cm + 8 cm = 20 cm

Through this method: P = a + b + c where P is the perimeter, for the length of the rectangle a and b is the width or some type (each side is equal).

P = 2(l + w) = 2(5) + 2(3) = 10 + 6 = 16 cm. The formula is 2l + 2w = 2(5) + 2(3) = 16

2. Circle: The perimeter of a circle is called the circumference. It is found by using the formula C = 2πr, where π is the circumference, r is a constant (approximately 3.14), and r is the radius of the circle.

Note that in the case of a square, triangle and rectangle, all the sides are equal in length and this is a more simpler case. However, for a circle the perimeter of a regular shape can be found in a more complex way.

Examples:

1.) Calculate the perimeter of a football field which measures 60 m by 30 m.

To calculate the perimeter of a football field, which measures 60 m by 30 m, you use the formula P = 2l + 2w, where l is the perimeter, l is the length, and w is the width. In this case, the length is 60 m and the width is 30 m, so the perimeter is 2(60) + 2(30) = 120 + 60 = 180 m.

2.) A rectangle has a perimeter of 34 m. Find the length of the rectangle if the breadth is 17 m.

To calculate the perimeter of a rectangle with a perimeter of 34 m and a breadth of 17 m, you can use the formula P = 2l + 2w, where P is the perimeter, l is the length, and w is the width. In this case, the perimeter is 34 m and the width is 17 m, so we can substitute these values into the formula: 34 = 2l + 2(17). Solving for l: 34 = 2l + 34, so 2l = 0, and l = 0 m.

3.) Calculate the perimeter of a square of side 13.9 m.

To calculate the perimeter of a square of side 13.9 m, you can use the formula P = 4s, where P is the perimeter and s is the side length. In this case, the side length is 13.9 m, so the perimeter is 4 × 13.9 = 55.6 m. Alternatively, you can add up the lengths of four sides of the square: the perimeter is 13.9 + 13.9 + 13.9 + 13.9 = 55.6 m.

4.) A square lawn has a perimeter of 56 m. Find the length of the side of the lawn.

To find the length of the side of a square lawn with a perimeter of 56 m, you can use the formula P = 4s, where P is the perimeter and s is the length of one side of the square. In this case, the perimeter is 56 m, so you can substitute this value into the formula: 56 = 4s. Solving for s: s = 56 ÷ 4 = 14 m.

5.) Calculate the circumference of a circle of radius 10.7 m. (Let π = 3.14*)

To calculate the circumference of a circle of radius 3.5 m, you can use the formula C = 2πr, where C is the circumference, π is a constant (approximately 3.14), and r is the radius of the circle. In this case, the radius is 10.7 m, so the circumference is 2 × 3.14 × 10.7 = 67.196 m.

Evaluation

1. What is the perimeter of a football field that measures 80 m by 50 m? 80×50 m 130 m or 260 m Answer: 260 m 
2. A rectangle has a perimeter of 74 m and a breadth of 17 m. What is the length of the rectangle? (a) 37 m (b) 20 m (c) 17 m (d) 54 m Answer: 20 m 
3. What is the perimeter of a square with a side of 12.3 cm? (a) 49 cm (b) 49.2 cm (c) 50 cm (d) 49 cm Answer: 49.2 cm 
4. A square lawn has a perimeter of 48 m. What is the length of one side of the square? (a) 12 m (b) 11 m (c) 10 m (d) 13 m Answer: 12 m 
5. What is the circumference of a circle with a radius of 10.0 m? 3.14×7? (a) 10 m (b) 20.14 m Answer: 62.8 m 
6. What is the perimeter of a square with a side of 4m? (a) 24m (b) 16m (c) 28m (d) 20m Answer: 16m 
7. A rectangle has a perimeter of 46 m and a width of 7m. What is the perimeter? (a) 46(b) 35 (c) 32 (d) 16m (e) Answer: 46m 
8. What is the perimeter of a circle with a diameter of 6m? (a) 6.16×m (b) 4.62m (c) 12.16m (d) 19.17m Answer: 18.84m 
9. A triangle has sides measuring 8 cm, 10 cm, and 12 cm. What is the perimeter? (a) 30 cm (b) 20 cm (c) 32 cm Answer: 30 cm 
10. What does a rectangle of 64 cm. What is one side length? (a) 4 cm (b) 8 cm (c) 6 cm (d) 10 cm Answer: 8 cm 

Perimeter of Irregular shapes

Irregular shapes are geometric shapes that do not have equal sides or angles. They are also called non-regular shapes. Unlike regular shapes, which have all sides and angles equal, irregular shapes have sides and angles of different lengths and measures.

To find the perimeter of an irregular shape, you need to add up the lengths of all the sides. Since irregular shapes can have sides of different lengths, you need to measure each side individually and then add them all together to get the total perimeter.

Perimeter of Irregular shapes

Irregular shapes are geometric shapes that do not have equal sides or angles. They are also called non-regular shapes. Examples of irregular shapes include shapes that have different side lengths or angles, or shapes that have curved sides. Unlike regular shapes, such as squares and circles, the perimeter of an irregular shape cannot be determined by a specific formula because all its sides have different lengths.

Irregular shapes can be found in many forms in nature and in man-made objects. They can be found in such things as rocks, leaves, clouds, and many other places. They are also used in many forms of art such as paintings, sculptures, and architecture.

In order to calculate the perimeter of an irregular shape, you need to measure the length of each side and then add those lengths together. Calculating is not the perimeter of an irregular shape because it requires the measurement of each side separately.

For example, it is often used to teach children how to measure and compare the lengths of different shapes, which is also an important mathematics for them. Appears to test the problem solving and reasoning skills of students.

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Examples:

1. An irregular shape has sides of length 60 cm, 80 cm, 70 cm, and 100 cm. To find the perimeter of this shape, you would measure all the sides and add them together. The perimeter = 60 + 80 + 70 + 100 = 310 cm. 
2. A triangular shape is formed by a trapezoid and a triangle. The trapezoid has a base of 60 cm and the top is 40 cm and a height of 30 cm. The triangle has sides of length 50 cm. To find the perimeter of this shape, you would measure the length of each side and then add them all together. The perimeter of this shape would be 60+40+50+50+30 = 230 cm. 
3. An irregular shape has sides of length 45 cm, 55 cm, 38 cm, 62 cm, and 73 cm. The fourth one has length of 60 cm and the fifth one has length of 70 cm. To find the perimeter of this shape, you would measure all the sides and add them together. The perimeter = 45 + 55 + 38 + 62 + 73 + 60 + 70 = 403 cm. 
4. An irregular shape is a combination of a circle and a triangle. The circle has a radius of 35 cm and the triangle has sides of length 40 cm, 50 cm, and 60 cm. To find the perimeter of this shape, you would measure the length of each side and then add them all together. The perimeter of this irregular shape would be 2π(35) + 40 + 50 + 60 = 70π + 150 = 70 × 3.14 + 150 = 219.8 + 150 = 369.8 cm. 
5. A hexagonal shape has sides of 50 cm each. This shape has 6 sides, so the perimeter can be formed by random lines. The perimeter of shape 6 is measured to be 300 cm and shape B is measured to be 150 cm. To find the perimeter of the shape, you can add the sides together. The perimeter of this irregular shape would be 300+150 = 450 cm. 

Importance of Perimeter in solving real life problems

Construction and Carpentry: The perimeter of a building is important to determine the amount of materials needed for construction and to calculate the cost of the project. Architects and builders also need to accurately measure perimeter to ensure that a building or structure meets safety and structural requirements.

Landscaping and Gardening: The perimeter of a lawn or garden is used to calculate the amount of fertilizer, seed, and other materials needed to maintain it. The perimeter is also used to determine how much fencing is being or needed to enclose a garden or lawn.

Security and Safety: Perimeter measurements are used in security systems to establish the boundaries of a property or facility. This information is used to determine where to place security cameras, lights, and other equipment. Perimeter measurements are also used to secure property and installations.

Logistics and Navigation: Perimeter measurements are used in logistics and transportation to determine the amount of space needed to store goods and materials. This information is used to plan the layout of warehouses and storage facilities. Perimeter measurements are also used in transportation systems used to plan routes, schedule deliveries, and manage inventory.

Sports and Recreation: Perimeter measurements are used in sports to design playing fields and courts. For example, the perimeter of a football field is used to determine the amount of grass seed needed for the field dimensions of fields, courts, and other playing surfaces. This information is used to establish rules and regulations, and to ensure fair play and competitions.

Science and Research: Scientists and researchers use perimeter measurements to create maps and to measure land for real estate and construction projects.

Industry and Agriculture: Perimeter measurements are used in industry and agriculture to calculate the area of equipment and the amount of land required for production. This information is used to make land manager decisions and to ensure the efficient use of resources.

Questions:

1. What is the perimeter of an irregular shape with sides of length 60 cm, 80 cm, 70 cm, and 100 cm? a) 300 cm (b) 280 cm (c) 350 cm (d) 310 cm 
2. A triangular shape is formed by combining a trapezoid and a triangle. The trapezoid has a base of 60 cm and the top is 40 cm and a height of 30 cm. The triangle has sides of length 50 cm. What is the perimeter of this shape? a) 280 cm (b) 240 cm (c) 260 cm (d) 270 cm 
3. An irregular shape has sides of length 45 cm, 55 cm, 38 cm, 62 cm, and 73 cm. What is the length of 50 cm, the fourth one has length of 60 cm and the fifth one has length of 70 cm. What is the perimeter of this shape? a) 380 cm (b) 390 cm (c) 400 cm (d) 403 cm 
4. An irregular shape is a combination of a circle and a triangle. The circle has a radius of 35 cm and the triangle has sides of length 60 cm, 50 cm and 60 cm. What is the perimeter of this shape? a) 264.4 cm (b) 369.8 cm (c) 400 cm (d) 350 cm 
5. An irregular shape is formed by connecting two irregular shapes, a shape A and shape B. It has a perimeter by random lines. The perimeter of shape A is measured to be 300 cm and shape B is measured to be 150 cm. What is the perimeter of this shape when they are joined together? a) 400 cm (b) 420 cm (c) 450 cm (d) 430 cm 
6. An irregular shape has sides of length 75cm, 50cm, 85cm, and 40cm. What is the perimeter of this shape? a) 130cm (b) 140cm (c) 180cm (d) 250cm 
7. An irregular shape is formed by connecting a square and a triangle. The rectangle has a length of 30 cm and a width of 20 cm. The triangle has sides of length 25 cm, 30 cm, and 35 cm. What is the perimeter of this shape? a) 170cm (b) 75cm (c) 200cm (d) 87cm 
8. An irregular shape has sides of length 15 cm and 5cm where shape is an ellipse. The square has a side of length 15 cm and the hexagon has side of length 10cm. What is the perimeter of this shape? a) 180 cm (b) 70 cm (c) 74 cm (d) 78 cm 
9. An irregular shape is formed by joining a hexagon and a pentagon. The ellipse has a major axis of 50 cm and a minor axis of 40 cm. The pentagon has sides of length 25 cm, 18, 22 and 30 cm. What is the perimeter of this shape? a) 115 cm (b) 125 cm (c) 138 cm (d) 123 cm 
10. An irregular shape has sides of length 40 cm, 55 cm, 35 cm, and 65 cm. What is the perimeter of this shape? a) 175 cm (b) 195 cm (c) 200 cm (d) 240 cm 

Lesson Presentation

Step 1:

Revision (5 min):

• Revise the last topic with the pupils which was Conventional Maths – Money (Simple Interest, Commission, Discount and Ratio)

Introduction (10 min):

• Begin the lesson by reviewing the concept of perimeter and its importance in real-life applications.
• Write the formula for finding the perimeter of a rectangle (P = 2l + 2w) on the whiteboard and have students solve the concept of perimeter using familiar shapes.

Step Instructions (20 min):

• Introduce the concept of irregular shapes and their specific formulas for finding perimeter (e.g., square = 4s, triangle = a + b + c, etc.)
• Provide examples of regular shapes and have students calculate the perimeter of each shape.
• Discuss the concept of irregular shapes and their characteristics (shapes that do not have equal sides or angles).

Guided Practice (20 min):

• Provide students with examples of irregular shapes and have them measure the length of each side using a ruler or measuring tape.
• Have students work in pairs to measure the perimeter of each irregular shape by adding the lengths of all the sides.

Independent Practice (10 min):

• Provide students with more examples of irregular shapes and have them calculate the perimeter of each shape individually.
• Monitor students’ progress and offer help as needed.

Conclusion (5 min):

• Review the key concepts of the lesson with students and have them share their answers to the independent practice problems.
• Summarize the lesson by emphasizing the importance of understanding perimeter in real-life applications.
• Assign homework or additional practice problems related to perimeter calculations.