Perimeter and Area | A

Question 2

Estimate and Verify

Take a rough sheet of paper or a sheet of newspaper. Make a few random shapes by cutting the paper in different ways. Estimate the total length of the boundaries of each shape then use a scale or measuring tape to measure and verify the perimeter for each shape.

Solution

We will learn to guess the boundary length of shapes and then check our guess.

Step 1 — Prepare the Shapes

Get a sheet of paper. You can use newspaper. Cut out a few shapes. Make them different. They can be irregular.

Diagram 1

Step 2 — Estimate the Perimeter

The perimeter is the total length around the shape. Look at one shape. Try to guess its perimeter. Break the boundary into small parts. Guess the length of each small part. Add all these guessed lengths. Write down your estimate.

$\boxed{\text{Your Estimated Perimeter}}$

Step 3 — Measure the Perimeter

Take a piece of string. Place the string along the edge of your shape. Make sure it follows all curves. Mark the start and end points on the string. Now, take the string. Stretch it out straight. Use a ruler or measuring tape. Measure the length of the string between your marks. This is the actual perimeter. Write down this measurement.

$\boxed{\text{Your Measured Perimeter}}$

Step 4 — Compare and Verify

Look at your estimated perimeter. Look at your measured perimeter. Are they close to each other? Your estimate should be near the actual measure. This shows how good your estimation skills are. You have verified your estimate.

Answer

(i) We estimate the perimeter by visually breaking the boundary into small parts and adding their guessed lengths. (ii) We measure the perimeter by using a string along the boundary and then measuring the string's length with a ruler. (iii) We verify by comparing the estimated and measured perimeters; they should be close.

More questions in A

Deep Dive: In races, usually there is a common finish line for all the runners. Here are two square running tracks with the inner track of 100 m each side and outer track of 150 m each side. The common finishing line for both runners is shown by the flags in the figure which are in the center of one of the sides of the tracks.

If the total race is of 350 m, then we have to find out where the starting positions of the two runners should be on these two tracks so that they both have a common finishing line after they run for 350 m. Mark the starting points of the runner on the inner track as ‘A’ and the runner on the outer track as ‘B’.

Estimate and Verify

Find various objects from your surroundings that have regular shapes and find their perimeters. Also, generalise your understanding for the perimeter of other regular polygons.

Draw a circle on a graph sheet with diameter (breadth) of length 3. Count the squares and use them to estimate the area of the circular region.

Try using different shapes (triangle and rectangle) to fill the given space (without overlaps and gaps) and find out the merits associated with using a square shape to find the area rather than another shape. List out the points that make a square the best shape to use to measure area.

Find the area (in square metres) of the floor outside of the corridor.

Find the area (in square metres) occupied by your school playground.

On a squared grid paper (1 square = 1 square unit), make as many rectangles as you can whose lengths and widths are a whole number of units such that the area of the rectangle is 24 square units.

a. Which rectangle has the greatest perimeter? b. Which rectangle has the least perimeter? c. If you take a rectangle of area 32 sq cm, what will your answers be? Given any area, is it possible to predict the shape of the rectangle with the greatest perimeter as well as the least perimeter? Give examples and reasons for your answer.

Draw a rectangle on a piece of paper and draw one of its diagonals. Cut the rectangle along that diagonal and get two triangles.

Check! whether the two triangles overlap each other exactly. Do they have the same area?

Try this with more rectangles having different dimensions. You can check this for a square as well.

Can you draw any inferences from this exercise? Please write it here.

Q10

Draw suitable triangles on grid paper to verify your inferences and relationships observed in the above exercises.