⇒ Perimeter = sum of lengths of all sides ⇒ Perimeter = sum of the length of all sides The formulas for calculating the perimeter and area of a triangle ABC are: The area for the park is shown in dark green color.Ĭalculating Area and Perimeter for Different Shapes Triangle To calculate the area for different shapes, use different formulas based on the number of sides and other characteristics such as angles between the sides. The area for a 2-dimensional shape is the space enclosed within the perimeter of the given shape. The peripheral border in blue is the perimeter of the park. For the figures with straight sides such as triangle, rectangle, square or a polygon the perimeter is the sum of lengths for all the sides. Perimeter for a 2-dimensional shape is the total distance around the respective shape. Calculating Area and Perimeter for Different Shapes.How can you be certain that no other perimeters could be made?įinish off the lesson by emphasising that when we join two shapes together the area of the new shape is the sum of the original areas, but the perimeter of the new shape depends on how much of the original shapes’ perimeters are touching.Why are all the perimeters even numbers?.How do you know that you have found the smallest/largest possible perimeter?.Here are some useful prompts for drawing the discussion together: If students are working on Polypad, you can share their work via the "Class" tab on Polypad. You could encourage students to share some of the shapes they found with the whole class and explain their reasoning. Towards the end of the lesson, bring the class together to share findings. At the end of this document is a diagram of all pentominoes with a side-length of 1 cm. It might be useful to keep the 12 pentominoes visible on the board or print a copy of the pentominoes so that students working on squared paper can remind themselves of the shapes they are working with. If students have their own devices, they can use the pen tool to annotate the shapes they make or the text tool to record the perimeters and areas. Give students some time to explore, reminding them of the importance of recording their findings so that they are ready to share with the class later. Which perimeters in between can you make?.What is the largest perimeter of a shape made by joining two pentominoes together?.What is the smallest perimeter of a shape made by joining two pentominoes together?.Once students have created a few examples, pose the following questions: Can students explain what’s different about this pentomino? Main Activity Most shapes have a perimeter of 12, except for the P-pentomino which has a perimeter of 10. They should notice that all shapes have the same area (5), but not the same perimeter. Invite students to calculate the area and the perimeter of each of the twelve pentominoes, and find the “odd one out”. Use Polypad to display all pentominoes, and enable the square grid to help students see the lengths of each side more clearly. If students haven’t seen pentominoes before, you may wish to start with a quick overview. Lesson objective: Understand that shapes with the same area can have different perimeter Lesson activity Warm-up This task explores the perimeter of shapes made from pentominoes, and offers students opportunities to work systematically and construct reasoned arguments. Pentominoes can be used recreationally to complete various puzzles. There are twelve different types, all of which are available as tiles within Polypad. A pentomino is a shape made up of 5 individual squares.
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