Perimeter and Area | IT

Question 5

Arrange the two pieces to form a figure with a perimeter of 22 cm.

Solution

Understand the Question

We are given two rectangular pieces, each measuring $5\text{ cm}$ in length and $1\text{ cm}$ in width.
When two shapes are joined together to form a single shape, the sides that touch become internal and are no longer part of the outer boundary (perimeter).
To obtain a perimeter of $22\text{ cm}$ , we need to determine how to join the two rectangles end-to-end.

Step 1 · Calculate Perimeter of One Rectangle

For a single rectangle with $\text{length} = 5\text{ cm}$ and $\text{width} = 1\text{ cm}$ :

\begin{aligned} \text{Perimeter} &= 2 \times (\text{length} + \text{width}) \\[0.6em] &= 2 \times (5\text{ cm} + 1\text{ cm}) \\[0.6em] &= 2 \times 6\text{ cm} \\[0.6em] &= 12\text{ cm} \end{aligned}

Two separate rectangles have a combined perimeter of $2 \times 12\text{ cm} = 24\text{ cm}$ .

Step 2 · Join the Rectangles Along the 1 cm Sides

Diagram 1

Place the two rectangles end-to-end such that their $1\text{ cm}$ sides touch.

The resulting figure is a single longer rectangle with:

$\text{New Length} = 5\text{ cm} + 5\text{ cm} = 10\text{ cm}$
$\text{New Width} = 1\text{ cm}$

Calculate the perimeter of the combined figure:

\begin{aligned} \text{Perimeter} &= 2 \times (\text{new length} + \text{new width}) \\[0.6em] &= 2 \times (10\text{ cm} + 1\text{ cm}) \\[0.6em] &= 2 \times 11\text{ cm} \\[0.6em] &= 22\text{ cm} \end{aligned}

Answer

Join the two rectangles end-to-end along their $1\text{ cm}$ sides to form a rectangle of dimensions $10\text{ cm} \times 1\text{ cm}$ , giving a perimeter of $22\text{ cm}$ .

Common Mistakes

Joining along the longer ( $5\text{ cm}$ ) side: Placing the rectangles side-by-side along the $5\text{ cm}$ side creates a $5\text{ cm} \times 2\text{ cm}$ rectangle with a perimeter of $2 \times (5 + 2) = 14\text{ cm}$ instead of $22\text{ cm}$ .
Forgetting to subtract shared edges: When combining two shapes, the shared contact edge disappears from both shapes, reducing the total perimeter by twice the length of the joined edge ( $24\text{ cm} - 2\text{ cm} = 22\text{ cm}$ ).

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Q18

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