Plane Shapes : Perimeter of Regular and Irregular Shapes

SUBJECT: MATHEMATICS

CLASS: BASIC FIVE / PRIMARY 5

TERM : SECOND TERM

WEEK : WEEK 8

TOPIC : Plane Shapes : Perimeter of Regular and Irregular Shapes

• Meaning of Perimeter
• Perimeter of regular plane shapes like rectangle, triangle, square and circle
• Perimeter of irregular plane shapes
• Real life problems on perimeter

Importance

• They help in quantifying physical space eg fencing plots of land, roofing of a house,
• They provide foundation or more advanced mathematics found in trigonometry, algebra, and calculus
• Real life problems on perimeter

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
• Relate perimeter to real life problem and solve them

Learning Activities :

• Pupils in pairs are asked to cut a polygon with measured shapes. They join the polygon together just to give a shape. After doing that, measure the total length around the shape being created
• Pupils in small groups use tape to measure to measure the perimeter of the desk in the class
• Pupils in small groups to use thread or fishing thread, cut into sizeable pieces to for on a Circle on a bottle. Distance round the bottle circle is the circumference. Then the thread or fishing thread is straightened to form a straight line, use ruler to measure the line. This is the perimeter of the circle.

Embedded Core Skills

• Critical thinking and problem solving skills
• Communication and Collaboration
• Student Leadership skills and Personal Development

Learning Resources

• Flash cards
• Formula of perimeters of shapes
• Cardboards to cut to different shapes
• Textbooks and Workbook with simple interest, discount, and commission 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 of the boundary of a shape. To find the perimeter of a shape, you add up the lengths of all the sides of the shape. It is usually measured in units such as inches, feet, or centimeters. It is commonly used in mathematics, specifically in geometry, to describe the size of a shape or the distance around it.

1. The perimeter of a square is the distance around the outside of the square. 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, the perimeter would be 5 + 5 + 5 + 5 = 20 units.
2. 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 a rectangle is 8 units and the width is 5 units, the perimeter would be 8 + 8 + 5 + 5 = 26 units.
3. 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 the three sides of a triangle are 5 units, 6 units, and 7 units, the perimeter would be 5 + 6 + 7 = 18 units.
4. The perimeter of a circle is called the circumference. To find the circumference, you 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. For example, if the radius of a circle is 5 units, the circumference would be 2π(5) = 31.4 units.
5. The perimeter of a hexagon is the distance around the outside of the hexagon. To find the perimeter, you add up the lengths of all six sides. For example, if the length of each side of a hexagon is 4 units, the perimeter would be 4+4+4+4+4+4 = 24 units
6. The perimeter of a octagon is the distance around the outside of the octagon. To find the perimeter, you add up the lengths of all eight sides. For example, if the length of each side of a octagon is 5 units, the perimeter would be 5+5+5+5+5+5+5+5 = 40 units
7. The perimeter of a parallelogram is the distance around the outside of the parallelogram. To find the perimeter, you add up the lengths of all four sides. For example, if the length of a parallelogram is 8 units and the width is 5 units, the perimeter would be 8 + 8 + 5 + 5 = 26 units
8. The perimeter of a rhombus is the distance around the outside of the rhombus. To find the perimeter, you add up the lengths of all four sides. For example, if the length of each side of a rhombus is 6 units, the perimeter would be 6+6+6+6= 24 units
9. The perimeter of a trapezoid is the distance around the outside of the trapezoid. To find the perimeter, you add up the lengths of all four sides. For example, if the length of the top side of a trapezoid is 10 units, bottom side is 8 units and the height is 5 units, the perimeter would be 10+8+5+5 = 28 units
10. The perimeter of an irregular shape can be found by measuring the length of each side and then adding them all together. For example, if an irregular shape has sides of length 6 units, 8 units, 9 units, and 10 units, the perimeter would be 6 + 8 + 9 + 10 = 33 units.

The perimeter of a regular plane shape is the distance around the outside of the shape. The formula for finding the perimeter of a shape can vary depending on the shape. Here are some examples of the formulas for finding the perimeter of regular plane shapes:

1. Rectangle: The perimeter of a rectangle is found by adding the lengths of all four sides. The formula is P = 2l + 2w, where P is the perimeter, l is the length of the rectangle, and w is the width of the rectangle.
2. Triangle: The perimeter of a triangle is found by adding the lengths of all three sides. The formula is P = a + b + c, where P is the perimeter, and a, b, and c are the lengths of the triangle’s sides.
3. Square: The perimeter of a square is found by adding the lengths of all four sides. The formula is P = 4s, where P is the perimeter and s is the length of one side of the square.
4. Circle: The perimeter of a circle is called the circumference. It is found by using the formula C = 2πr, where C is the circumference, π 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 thus it is a regular shape, while in the case of a circle it is always a regular shape as all points on the circumference are equidistant from the center.

Examples

(1.) Calculate the perimeter of a football field which measures 80 m by 50 m.

To calculate the perimeter of a football field which measures 80 m by 50 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 length is 80 m and the width is 50 m, so the perimeter is 2(80) + 2(50) = 160 + 100 = 260 m.

(2)A rectangle has a perimeter of 74 m. Find the length of the rectangle if its breadth is 17 m.

A rectangle has a perimeter of 74 m and the breadth is 17 m. To find the length of the rectangle, 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 breadth is known (17 m), so we can substitute it into the formula and solve for the length. 74 = 2l + 2(17) => l = (74 – 34) / 2 => l = 20 m

(3)Calculate the perimeter of a square of side 12.3 cm.

To calculate the perimeter of a square of side 12.3 cm, 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 length of one side of the square is 12.3 cm, so the perimeter of the square is 4 x 12.3 cm = 49.2 cm.

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

A square lawn has a perimeter of 56 m. To find the length of the side of the lawn, 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 solve for s by dividing the perimeter by 4. s = 56/4 = 14 m

(5)Calculate the circumference of a circle of radius 31/2 m. (Let π = 31/7).

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 (31/7), and r is the radius of the circle. In this case, the radius is 3.5 m, so the circumference is 2 x (31/7) x 3.5 = 31 x 5/7 = 155/7 = 22.14 m.

Evaluation

1. What is the perimeter of a football field that measures 80 m by 50 m? a) 260 m b) 150 m c) 200 m d) 280 m
2. A rectangle has a perimeter of 74 m and a breadth of 17 m. What is the length of the rectangle? a) 20 m b) 15 m c) 25 m d) 30 m
3. What is the perimeter of a square with a side of 12.3 cm? a) 48 cm b) 49.2 cm c) 50 cm d) 45 cm
4. A square lawn has a perimeter of 56 m. What is the length of the side of the lawn? a) 14 m b) 12 m c) 16 m d) 18 m
5. What is the circumference of a circle with a radius of 31/2 m (let π = 31/7)? a) 20.5 m b) 22.14 m c) 19 m d) 25 m
6. What is the perimeter of a square with a side of 5m? a) 20m b) 15m c) 25m d) 30m
7. A rectangle has a length of 15m and a width of 7m, what is its perimeter? a) 34m b) 36m c) 32m d) 30m
8. What is the perimeter of a circle with a diameter of 6m? a) 18.85m b) 9.42m c) 12.57m d) 15.71m
9. A triangle has sides of length 5m, 7m, and 8m. What is its perimeter? a) 20m b) 18m c) 15m d) 22m
10. A square has a perimeter of 24 cm. What is its side length? a) 6 cm b) 8 cm c) 4 cm d) 10 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. 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 rocks, leaves, clouds, and many other places. They are also used in many forms of art, such as painting, sculpture and photography.

In order to calculate the perimeter of an irregular shape, you need to measure the length of each side and then add them all together. It can be challenging to find the perimeter of an irregular shape because it requires the measurement of each side separately.

In mathematics, it’s often used to teach children how to measure and compare the lengths of different shapes, but also it’s used in advanced mathematics for other purposes such as finding the area of a shape

1. An irregular shape has sides of length 60 cm, 80 cm, 90 cm, and 100 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 60 + 80 + 90 + 100 = 330 cm.
2. A irregular shape is formed by a trapezoid and a triangle. The trapezoid has a base of 60 cm and 80 cm and a height of 50 cm. The triangle has sides of length 30, 40 and 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 irregular shape would be 60+80+30+40+50 = 260 cm
3. An irregular shape is a polygon with five sides, three of the sides have the length of 50 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 the length of each side and then add them all together. The perimeter of this irregular shape would be 50+50+50+60+70 = 280 cm
4. An irregular shape is a combination of a circle and a triangle. The circle has a radius of 30 cm and the triangle has sides of length 40, 50 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 2πr + 40+50+60 = 2π(30) + 150 = 150 + 94.2 = 244.2 cm
5. An irregular shape is formed by connecting two irregular shapes, a shape A and shape B, that are formed by random lines. The perimeter of shape A is measured to be 200 cm and shape B is measured to be 150 cm. To find the perimeter of this shape, you would add the perimeter of shape A and shape B together. The perimeter of this irregular shape would be 200+150 = 350 cm.

Importance of Perimeter in solving real life problems

1. Construction and Architecture: The perimeter of a building or structure is used to determine the amount of materials needed for construction and to calculate the cost of the project. Architects and builders also use perimeter measurements to ensure that a building or structure meets local zoning and building codes.
2. 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 or edging is needed to enclose the area.
3. Security: Perimeter measurements are used in security systems to establish the boundaries of a property or facility. This information is used to set up cameras, alarms, and other security measures to protect the property and its inhabitants.
4. Logistics and Transportation: Perimeter measurements are used in logistics and transportation to calculate the amount of space required for storage and the amount of fuel needed for a trip. This information is used to plan routes, schedule deliveries, and manage inventory.
5. Sports and Recreation: Perimeter measurements are used in sports and recreation to determine the dimensions of fields, courts, and other playing surfaces. This information is used to establish rules and regulations for games and competitions.
6. Surveying and Mapping: Surveyors use perimeter measurements to create maps and to measure land for real estate and construction projects.
7. Industry and Agriculture: Perimeter measurements are used in industry and agriculture to measure the size of equipment and the amount of land required for production. This information is used to plan and manage operations, and to calculate costs and revenues.

1. What is the perimeter of an irregular shape with sides of length 60 cm, 80 cm, 90 cm, and 100 cm? a) 330 cm b) 280 cm c) 360 cm d) 320 cm
2. An irregular shape is formed by a trapezoid and a triangle. The trapezoid has a base of 60 cm and 80 cm and a height of 50 cm. The triangle has sides of length 30, 40 and 50 cm. What is the perimeter of this shape? a) 260 cm b) 250 cm c) 240 cm d) 270 cm
3. An irregular shape is a polygon with five sides, three of the sides have 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) 280 cm b) 260 cm c) 250 cm d) 270 cm
4. An irregular shape is a combination of a circle and a triangle. The circle has a radius of 30 cm and the triangle has sides of length 40, 50 and 60 cm. What is the perimeter of this shape? a) 244.2 cm b) 250 cm c) 260 cm d) 240 cm
5. An irregular shape is formed by connecting two irregular shapes, a shape A and shape B, that are formed by random lines. The perimeter of shape A is measured to be 200 cm and shape B is measured to be 150 cm. What is the perimeter of this shape? a) 350 cm b) 340 cm c) 360 cm d) 330 cm
6. An irregular shape has sides of length 25cm, 35cm, 30cm, and 40cm. What is the perimeter of this shape? a) 130cm b) 140cm c) 150cm d) 120cm
7. An irregular shape is a combination of a rectangle and a triangle. The rectangle has a length of 20 cm and width of 25cm. The triangle has sides of length 10, 12 and 15 cm. What is the perimeter of this shape? a) 77cm b) 72cm c) 82cm d) 87cm
8. An irregular shape is formed by connecting a square and a hexagon. The square has a side of length 15 cm and the hexagon has side of length 12cm. What is the perimeter of this shape? a) 69 cm b) 72 cm c) 74 cm d) 78 cm
9. An irregular shape is a combination of an ellipse and a pentagon. The ellipse has a major axis of 30 cm and a minor axis of 20 cm. The pentagon has sides of length 25, 20, 18, 22 and 30 cm. What is the perimeter of this shape? a) 115 cm b) 125 cm c) 130 cm d) 120 cm
10. An irregular shape has sides of length 40 cm, 50 cm, 55 cm, and 65 cm. What is the perimeter of this shape? a) 210 cm b) 220 cm c) 230 cm d) 240 cm

Lesson Presentation

Step 1 :

Revision (5 min);

• Revise the last topic with the pupils which was Commercial Maths : Money Simple Interest, Discount and Commission, Money Transaction

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 a few examples of rectangles with different dimensions.

Direct Instruction (20 min):

• Introduce the concept of regular 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.
• Review the concept of irregular shapes and their characteristics (shapes that do not have equal sides or angles).

Guided Practice (20 min):

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

Independent Practice (15 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 highlighting the importance of understanding perimeter in real-life applications.
• Assign any homework or additional practice problems related to perimeter