Perimeter and Area | IT

Question 5

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

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Solution

IT-5

Chapter: PERIMETER AND AREA
Class: 6 (Class 6)
Category: in_text

Question

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

Question diagram(s):

Question diagram

We have two pieces. Each piece is a rectangle that is 5 cm long and 1 cm wide. We need to arrange these two pieces to make a new shape. The new shape must have a perimeter of 22 cm.

Let us find the perimeter of one rectangle first. Length of one rectangle = 5 cm. Width of one rectangle = 1 cm.

Step 1 — Find the perimeter of one rectangle

The perimeter of a rectangle is found by adding all its side lengths. Perimeter = length + width + length + width Perimeter = 2×(length+width)2 \times (\text{length} + \text{width})

=2×(5 cm+1 cm)= 2 \times (5 \text{ cm} + 1 \text{ cm})

=2×6 cm= 2 \times 6 \text{ cm}

12 cm\boxed{12 \text{ cm}}

So, one rectangle has a perimeter of 12 cm. Two separate rectangles would have a total perimeter of 2×12=24 cm2 \times 12 = 24 \text{ cm}.

Step 2 — Arrange the two rectangles

We need to arrange the two rectangles so the total perimeter is 22 cm. This means we must overlap them. When we overlap them, some parts of their edges will be hidden inside the new shape. These hidden parts do not count towards the perimeter.

Let us place the two rectangles side-by-side along their 1 cm sides. Imagine one rectangle is placed horizontally. It is 5 cm long and 1 cm wide. We place the second rectangle next to it, also horizontally. The two 1 cm sides touch each other. These two 1 cm sides become hidden. The new shape will be a longer rectangle. Its new length will be 5 cm+5 cm=10 cm5 \text{ cm} + 5 \text{ cm} = 10 \text{ cm}. Its width will still be 1 cm.

Let us calculate the perimeter of this new combined rectangle. Perimeter = 2×(new length+new width)2 \times (\text{new length} + \text{new width})

=2×(10 cm+1 cm)= 2 \times (10 \text{ cm} + 1 \text{ cm})

=2×11 cm= 2 \times 11 \text{ cm}

22 cm\boxed{22 \text{ cm}}

This arrangement gives a perimeter of 22 cm.

Diagram 1

Answer

The two pieces, which are 5 cm by 1 cm rectangles, can be arranged by placing them side-by-side along their 1 cm sides. This forms a larger rectangle that is 10 cm long and 1 cm wide. The perimeter of this new shape is 22 cm.

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