Question 14
Let's do something tricky now! We have a figure below having perimeter 24 units.
Without calculating all over again, observe, think and find out what will be the change in the perimeter if a new square is attached as shown on the right.
When a new square is added, some old boundary lines become hidden, and some new boundary lines appear.
Step 1 — Understand the original shape
The first picture shows a cross shape. It is made of 5 small squares. Let us count the boundary lines of this cross shape. We can trace the outside edges. There are 12 outside edges. The problem tells us the perimeter is 24 units. So, each outside edge must be 2 units long. This means each small square has a side length of 2 units.
Step 2 — Observe how the new square is attached
Look at the second picture. A new small square is added. It is attached to the bottom-right part of the cross. The arrow shows it moving into place. This new square touches two parts of the original cross. It touches the bottom side of the rightmost square. It also touches the right side of the bottommost square.
Step 3 — Find the change in perimeter
When the new square is attached: Two sides of the original cross shape become hidden. These are the bottom side of the rightmost square and the right side of the bottommost square. Each of these hidden sides was part of the perimeter. So, the perimeter loses 2 sides. This means the perimeter decreases by:
The new square itself has 4 sides. Two of its sides are now hidden (its top side and its left side). Two of its sides are now part of the new perimeter (its bottom side and its right side). So, the new square adds 2 new sides to the perimeter. This means the perimeter increases by:
Step 4 — Calculate the total change
The perimeter decreased by 4 units because old sides became hidden. The perimeter increased by 4 units because new sides appeared. Let us find the total change.
Answer
(i) stays the same.
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Let's do something tricky now! We have a figure below having perimeter 24 units.
Without calculating all over again, observe, think and find out what will be the change in the perimeter if a new square is attached as shown on the right.
Experiment placing this new square at different places and think what the change in perimeter will be. Can you place the square so that the perimeter: a) increases; b) decreases; c) stays the same?
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a. Find the missing measurements.
b. Find out the area of his house.
Now, find out the missing dimensions and area of Sharan's home. Below is the plan:
Some of the measurements are given.
a. Find the missing measurements.
b. Find out the area of his house.
What are the dimensions of all the different rooms in Sharan's house? Compare the areas and perimeters of Sharan's house and Charan's house.
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In each figure, find the missing value of either the length of a side or the area of a region.