Perimeter and Area | IT

Question 4

Split and rejoin

A rectangular paper chit of dimension $6\text{ cm} \times 4\text{ cm}$ is cut as shown into two equal pieces. These two pieces are joined in different ways.

Find out the length of the boundary (i.e., the perimeter) of each of the other arrangements below.

Solution

Understand the Question

A rectangular sheet of dimension $6\text{ cm} \times 4\text{ cm}$ is cut into two equal rectangular pieces, each measuring $6\text{ cm} \times 2\text{ cm}$ .
The perimeter is the total distance around the outside boundary of the shape.
When two pieces are joined, the shared contact edge lies inside the shape and is not counted as part of the perimeter.

(a) Find the length of the boundary (perimeter) of arrangement (a).

Step 1 · Calculate Perimeter of Shape (a)

The two $6\text{ cm} \times 2\text{ cm}$ rectangles are joined end-to-end to form a single rectangle. Diagram 1

\begin{aligned} \text{Length of new rectangle} &= 6\text{ cm} + 6\text{ cm} = 12\text{ cm} \\[0.6em] \text{Width of new rectangle} &= 2\text{ cm} \end{aligned}

\begin{aligned} \text{Perimeter} &= 2 \times (\text{Length} + \text{Width}) \\[0.6em] &= 2 \times (12\text{ cm} + 2\text{ cm}) \\[0.6em] &= 2 \times 14\text{ cm} \\[0.6em] &= 28\text{ cm} \end{aligned}

Answer

(a) $28\text{ cm}$

(b) Find the length of the boundary (perimeter) of arrangement (b).

Step 1 · Calculate Perimeter of Shape (b)

The two $6\text{ cm} \times 2\text{ cm}$ pieces are joined into an L-shape. Adding all the outer boundary segments together:$$ \begin{aligned} \text{Perimeter} &= 6\text{ cm} + 8\text{ cm} + 2\text{ cm} + 6\text{ cm} + 4\text{ cm} + 4\text{ cm} \[0.6em] &= 30\text{ cm} \end{aligned}

Answer

(b) $30\text{ cm}$

Common Mistakes

Counting Inner Edges: Simply adding the perimeters of the two separate pieces ( $16\text{ cm} + 16\text{ cm} = 32\text{ cm}$ ) without subtracting the overlapping boundary inside the shape.
Missing Inner Step Edges: For composite/L-shaped arrangements, forgetting to account for the inner corner segments ( $4\text{ cm}$ each) when summing the boundary.

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Split and rejoin

A rectangular paper chit of dimension $6\text{ cm} \times 4\text{ cm}$ is cut as shown into two equal pieces. These two pieces are joined in different ways.

Find out the length of the boundary (i.e., the perimeter) of each of the other arrangements below.

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Find the area of the following figures.

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Can you see some relationship between the blue rectangle and the yellow triangle and their areas? Write the relationship here.

Q10

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Q11

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Q12

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Q13

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Q14

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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.

Q15

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Q16

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Q17

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Some of the measurements are given.

a. Find the missing measurements.

b. Find out the area of his house.

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Q18

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