As we know, perimeter and area have many applications, such as finding the area of the paths, roads etc. To solve the problem related to perimeter and area, follow some steps to solve it easily. A constructor has his land in the shape of the polygon shown below.
Find the area and the perimeter of the given figure. Ans: The perimeter of the closed figure is nothing but the sum of the lengths of the boundaries. The area of the given figure is the sum of the areas of the rectangle and the scalene triangle. Keerthi is planting a garden with the dimensions as shown below. Find the area of the roads. Calculate its circumference. Find the area of the farm. In this article, we have studied the definitions of the perimeter and the area of the figures. This article gives the applications and importance of the perimeter and the area.
This article also gives the solved examples that help us to solve the problems easily. Learn About Area and Perimeter of Triangles. What are the applications of the perimeter? Ans: The perimeter is used to find the total length of the boundary of any shape or figure.
What are the applications of the area? Fabric used for clothing and other items also demand that length and width be considered. The simplest and most commonly used area calculations are for squares and rectangles. To find the area of a rectangle, multiply its height by its width. For a square you only need to find the length of one of the sides as each side is the same length and then multiply this by itself to find the area.
Area and perimeter are two important and fundamental parts of mathematics. They are the foundation for understanding other aspects of geometry such as volume and mathematical theorems that help us understand algebra, trigonometry, and calculus. The perimeter of the irregular shape is equal to the sum of the six segment around the outside of the figure. To find the perimeter, we simply add up the lengths of each outside edge. It may be helpful to look out for number bonds when adding the sides.
The total of all of the outer sides is 36, so the perimeter is 36 cm. A square metre is defined as the area that is enclosed by a square, with sides measuring 1 metre. One sq m is equal to While residential plots are generally measured in sq ft, agricultural land is measured in acres. In geometry, the area can be defined as the space occupied by a flat shape or the surface of an object.
The area of a figure is the number of unit squares that cover the surface of a closed figure. Area is measured in square units such as square centimteres, square feet, square inches, etc. Why is the area of a square a side square?
A square is a 2D figure in which all the sides are of equal measure. Hence, the area of a square is side square. About Transcript. Perimeter is the distance around the outside of a shape. They wanted to calculate it using formulae. But I insisted, and asked students to come to the blackboard to show with their hands and fingers the area and perimeter.
One of the misconceptions that surprised me was when a student pointed to the longest length and the longest height and said that was the area, suggesting that they actually did not know what area is.
So I am really pleased I persevered and did not just tell them, or point out what the area and perimeter were. When I asked the students to find the area of the combined shape, at first some of the students were puzzled.
Some of the students even partitioned the shape into rectangles and squares and calculated the area of these using the formula that they remembered. So I prompted them to think of another method that would work. Student Sarika and her group then suggested counting the squares.
Once that idea had been explored and demonstrated with the whole class I asked the students to make at least three shapes with an area of 12 cm 2. I was amazed at the number of examples the students came up with, and their complexity.
The activity also made me think about tweaking tasks that I know are good and rich to turn them into other rich tasks. In the coming weeks I will put aside the tasks I use that I think are rich, and think about how I could tweak them so I can also use them as rich tasks for teaching other mathematical concepts. One of the issues when learning about area and perimeter is students not understanding the distinction between the two concepts.
This seems to affect even mature students. Reinke reported that when elementary pre-service teachers were asked to find the perimeter and area of a shaded geometric figure, many of them incorrectly used the same method for finding both perimeter and area. To make students aware of this distinction, in the next activity you will use the same structure as previous activities but slightly tweaked.
You then ask the students to construct first shapes that have the same area but different perimeters, and then shapes which have the same perimeter but different areas.
The first question was done quite quickly and with great enthusiasm. Once they had realised that they could rearrange the unit squares as they wanted, they could easily make squares with the same area.
Some students came up with a further question: coming up with shapes with the same area and perimeter. This led to a heated discussion about measurements and dimensions; that perimeter and area could not be the same because perimeter is expressed in a one-dimensional measurement cm and area is two-dimensional and expressed in cm 2. I also noted that the students looked back at the earlier examples they had made in the previous activities, linking their previous learning to the new learning — I liked that.
It also made it easier for them to access the second question and explore it. In the last section you focused on the measurements used in working out area and perimeter. Students tend to be told to use units of measurements such as metres, centimetres, inches, etc.
A unit of measurement is a measure defined and adopted as a standard by convention or by law, such as a metre, a gram or a litre. In the next activity you will ask your students to explore in groups any areas and perimeters they can find outside the classroom using their own measures, and then to compare and discuss their findings with other students in the class.
Taking the mathematics outside of the classroom in this way also allows the students to become aware that mathematics is all around us. At the same time, it gives them the opportunity to experience working with larger shapes than pencil and paper allow. This out-of-the-classroom activity works well when students work in groups of four or five and they have been assigned roles within their groups. For example, two students can be asked to measure, one student to oversee, one or two students to record the observations.
If your students have access to digital cameras or mobile phones with an integral camera, these could be used to take photographs of the shapes that the students measure in their groups.
Alternatively, a tape recorder could be used to record the measurements instead of writing them down when the students are working out-of-the-classroom. The task you are asking the students to do is to measure and work out the perimeter of as many large shapes as they can within a certain time period outside of the classroom.
For example, they could measure the perimeter and area of the playground, the flower bed, the water pump area. Decide with the students on a list of which shapes to measure so that the measurements can be compared later. Ask the students whether they came up with the same measurements. What was the same and what was different? Did they encounter any difficulties when measuring? Can they think of more effective and accurate ways to make such measurements? The class thought it would be very easy to complete this activity but when they actually started they found that there were a lot of challenges.
Some used a piece of wood they found, some used their tread length, some used their arm length and so on. During the discussion we found that the pupils had been wondering what to write for units.
They came up with the suggestion themselves that using standard units of measurement might be a good idea! During the discussion, the students talked about aspects of dimension as well as different dimensional measurements in a playful way, such as describing the area in twig 2!
This unit has focused on exploring the mathematical concepts of area and perimeter by helping the students to develop an understanding of and distinction between the concepts. The activities asked the students to use examples and objects that they can find around them and build on their intuitive understanding. In reading this unit you will have thought about how to enable your students to create examples themselves, think mathematically and reflect on the thinking processes involved. You will also have considered how to help your students to understand the concepts of area and perimeter by learning through talking in pairs, in groups and in whole-class discussions.
Identify three ideas that you have used in this unit that would also work well when teaching other topics. Make a note of two topics that you have to teach soon where those ideas can be used with some small adjustments.
Pair work is about involving all. Since students are different, pairs must be managed so that everyone knows what they have to do, what they are learning and what your expectations are. To establish pair work routines in your classroom, you should do the following:.
During pair work, tell students how much time they have for each task and give regular time checks. Praise pairs who help each other and stay on task. Give pairs time to settle and find their own solutions — it can be tempting to get involved too quickly before students have had time to think and show what they can do.
Most students enjoy the atmosphere of everyone talking and working. As you move around the class observing and listening, make notes of who is comfortable together, be alert to anyone who is not included, and note any common errors, good ideas or summary points. At the end of the task you have a role in making connections between what the students have developed. You may select some pairs to show their work, or you may summarise this for them.
Students like to feel a sense of achievement when working together. This might be an opportunity for students who are usually timid about contributing to build their confidence.
If you have given students a problem to solve, you could give a model answer and then ask them to discuss in pairs how to improve their answer. This will help them to think about their own learning and to learn from their mistakes. If you are new to pair work, it is important to make notes on any changes you want to make to the task, timing or combinations of pairs.
This is important because this is how you will learn and how you will improve your teaching. Organising successful pair work is linked to clear instructions and good time management, as well as succinct summarising — this all takes practice. Every effort has been made to contact copyright owners. If any have been inadvertently overlooked the publishers will be pleased to make the necessary arrangements at the first opportunity. Video including video stills : thanks are extended to the teacher educators, headteachers, teachers and students across India who worked with The Open University in the productions.
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