Activities on Perimeter & Area(A)

These activities are for understanding the inter-relation area & perimeter concepts

1. Take a rectangular piece of thick chart paper

   1. Cut it along the diagonal into 2 pieces – what can you say about these 2 shapes (right angled scalene triangles, both are congruent)

   2. Join both the pieces in as many ways as possible, keeping in mind that

      1. The 2 pieces should not overlap

      2. The resulting shape should only be a 3 or 4 sided figure

   3. How many different shapes have you been able to get?

   4. Can you name these shapes? (2 isosceles triangles, 1 rectangle, 2 parallelograms, 1 kite)

   5. Can you define the properties of these shapes?

   6. Can you name a property which all these shapes share? (area)

   7. Can you name a property which these shapes do not share? (perimeter)

   8. <a name="_Hlk15982128">(Can you arrange the figures in increasing order of their perimeters)</a>

2. Cut a scalene triangle

   1. Fold it into a rectangle

   2. Find out the area of the triangle

3. Cut 4 congruent scalene triangles

   1. Prove that 3 angles of a triangle is a straight angle

   2. Arrange the 4 triangles so that they form a larger but similar triangle

   3. From the above arrangement, find out how to cut any triangle into 4 smaller similar triangles

4. Cut a long rectangular piece of paper which looks like a ribbon.

   1. Gently fold a pentagon by tying a knot in the ribbon

5. Draw a circle

   1. Keeping the arms of a compass equal to the radius of the circle, mark off equal points on the circumference

   2. Join every point to the next point. What shape do you get? (Hexagon)

   3. Join every point to every other point.

   4. What other shapes do you see? (Equilateral triangles, rhombus/ parallelogram, trapezium)

   5. Find the sum of the angles in any of the triangles & quadrilaterals.

   6. What is the perimeter of the large shape? (6R)

   7. So what can you say about the circumference of the circle in comparison to the perimeter of the large shape?

6. Take 5 squares of equal size made from cardboard

   1. Join all the 5 squares into various shapes, keeping in mind that

      1. Any square should at least touch one other square along one side

      2. “Touching” means touching along the entire side. Touching partially is not allowed

      3. Touching just at the corners is not allowed.

   2. Each of these shapes is called a Pentomino. Penta means 5.

   3. On a dotted sheet, drawn each of the pentominoes you get

   4. What is the total number of shapes you can get? (12)

   5. Which of these pentominoes, if drawn on paper, can be folded into an open box?

   6. What is a property which is common to all these pentominoes? (area)

   7. Which is a property which all these pentominoes do not share? (perimeter)

   8. (Can you arrange the figures in increasing order of their perimeters)

7. Take the set of triangles (this has to be prepared in advance)

   1. Can you find if there are 2 triangles which are congruent?

   2. Can you find out if there are 2 triangles which are similar to each other?

8. Take the set of rectangles (this has to be prepared in advance)

   1. Without measuring, can you find out if there are 2 rectangles which are similar to each other? (If we keep the 2 similar rectangles overlapping and touching at one of the corners and along the 2 sides, their diagonals will coincide.