This document defines perimeter and explains how to calculate the perimeter of common shapes such as rectangles, triangles, circles, and composite shapes. It provides examples of calculating perimeters of various shapes, including word problems involving finding the total length of paths, boxes, photographs, and picture frames given measurements of the sides or diameters. The key points are that perimeter is the distance around an object and is calculated by adding all the lengths of the sides for simple shapes or the outer lengths for composite shapes.

1. PERIMETER
COMPOUND SHAPES

2. WHAT IS
PERIMETER?
P e r i m e t e r i s t h e
d i s t a n c e a r o u n d a n
o b j e c t .
Add a Footer 2

3. PERIMETER OF
COMMON SHAPES
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4. EXAMPLES
The table gives
measurements for
some rectangles.
Fill in the missing
values.
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Length Width Perimeter
1) 4 𝑐𝑚 12 𝑐𝑚
2) 5 𝑚𝑚 60 𝑚𝑚
3) 5 𝑐𝑚 14 𝑐𝑚
4) 7 𝑐𝑚 8 𝑐𝑚
5) 3 𝑚 6 𝑚

5. 1 ) 𝑃 = 2 𝑙 + 𝑏
1 2 = 2 4 + 𝑏
1 2 = 8 + 2 𝑏
2 𝑏 = 1 2 − 8 = 4
𝑏 =
4
2
= 𝟐
2 ) 𝑃 = 2 𝑙 + 𝑏
6 0 = 2 𝑙 + 5
6 0 = 2 𝑙 + 1 0
2 𝑙 = 6 0 − 1 0 = 5 0
𝑙 =
5 0
2
= 𝟐 𝟓
3 ) 𝑃 = 2 ( 𝑙 + 𝑏 )
1 4 = 2 ( 5 + 𝑏 )
1 4 = 1 0 + 2 𝑏
2 𝑏 = 1 4 − 1 0 = 4
𝑏 =
4
2
= 𝟐
4 ) 𝑃 = 2 ( 𝑙 + 𝑏 )
𝑃 = 2 ( 7 + 8 )
= 2 ( 1 5 )
𝑃 = 𝟑 𝟎
5 ) 𝑃 = 2 ( 𝑙 + 𝑏 )
𝑃 = 2 6 + 3
= 2 ( 9 )
𝑃 = 𝟏 𝟖
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Length Width Perimeter
1) 4 𝑐𝑚 𝟐 𝒄𝒎 12 𝑐𝑚
2) 𝟐𝟓 𝒎𝒎 5 𝑚𝑚 60 𝑚𝑚
3) 5 𝑐𝑚 𝟐 𝒄𝒎 14 𝑐𝑚
4) 7 𝑐𝑚 8 𝑐𝑚 𝟑𝟎 𝒄𝒎
5) 6 𝑚 3 𝑚 𝟏𝟖 𝒎
SOLUTIONS:

6. EXAMPLE
W h a t i s t h e p e r i m e t e r o f t h e
f i g u r e s h o w n o n t h e r i g h t ?
To find the perimeter, we must add up all the lengths
around the edges of the shape.
We must calculate the unknown lengths, 𝑥 𝑎𝑛𝑑 𝑦.
Now, the length of the entire side is 6 𝑐𝑚 and the length of
the shorter side is 4 𝑐𝑚. Therefore, to get the value of
𝑥, subtract.
𝑥 = 6 − 4 = 2 𝑐𝑚
Similarly, subtract to get the value of 𝑦.
𝑦 = 6 − 4 = 2 𝑐𝑚
Perimeter = 6 + 6 + 2 + 2 + 4 + 4 = 𝟐𝟒 𝒄𝒎
6
𝒙
𝒚

7. EXAMPLE
W h a t i s t h e p e r i m e t e r o f
t h e f i g u r e s h o w n o n t h e
r i g h t ?
To find the perimeter, we must add up all the lengths around the
edges of the shape.
We must calculate the unknown lengths, 𝑝, 𝑞, 𝑟 𝑎𝑛𝑑 𝑠.
𝑝 is the total height, 𝑝 = 7𝑚
𝑞 = 3𝑚
𝑟 = 2𝑚
𝑠 = 4 𝑚
Perimeter = 7 + 4 + 1 + 3 + 2 + 2 + 1 + 2 + 2 + 3 + 1 + 4
= 𝟑𝟐 𝒎
7
𝒑
𝒒
𝒓
𝒔

8. EXAMPLE
C a l c u l a t e t h e p e r i m e t e r
o f t h e f i g u r e s h o w n .
Remember that in calculating perimeter,
inside lengths are ignored.
Add all outside lengths.
𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟
= 18.1 + 11.1 + 4.3 + 12.1 + 12.1 + 4.3 + 11.1
= 𝟕𝟑. 𝟏 𝒌𝒎
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9. EXAMPLE
C a l c u l a t e t h e p e r i m e t e r
o f t h e f i g u r e s h o w n .
Remember that in calculating perimeter, inside lengths are
ignored.
Add all outside lengths.
Circumference of circle = 2𝜋𝑟 𝜋 =
22
7
= 2 ×
22
7
× 10.1 = 63.5 𝑚𝑚
Since we half a semi-circle, this value must be divided by two.
The length 𝐵𝐶 = 3.1 𝑚𝑚
The length 𝐴𝐵 = 20.2 𝑚𝑚
𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 =
63.5
2
+ 3.1 + 20.2 + 3.1 = 𝟓𝟖. 𝟐 𝒎𝒎 to 1 d.p.
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10. • Elizabeth is going to make a triangular path in her
garden. The sides will be 20 metres, 36 metres, and
18 metres. What is the total length of the path?
𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 𝑜𝑓 𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒 = 𝑎 + 𝑏 + 𝑐
𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 𝑜𝑓 𝑡𝑟𝑖𝑎𝑛𝑔𝑢𝑙𝑎𝑟 𝑝𝑎𝑡ℎ = 20 + 36 + 18
= 74 𝑚
Therefore the total length of the path = 𝟕𝟒 𝒎
WORD PROBLEMS
• Johanna is building 2 square planter boxes
in her garden. Each box is 2 metres wide.
What is the total perimeter of the boxes?
𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 𝑜𝑓 𝑠𝑞𝑢𝑎𝑟𝑒 = 𝑠𝑖𝑑𝑒 × 4
𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 𝑜𝑓 𝑝𝑙𝑎𝑛𝑡𝑒𝑟 = 2 × 4 = 8𝑚
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑞𝑢𝑎𝑟𝑒 𝑝𝑙𝑎𝑛𝑡𝑒𝑟𝑠 = 2
𝑇𝑜𝑡𝑎𝑙 𝑝𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 𝑜𝑓 𝑏𝑜𝑥𝑒𝑠 = 2 × 8𝑚 = 𝟏𝟔𝒎
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11. • Trina hung a rectangular photograph with
decorative tape along the whole perimeter. She
used 24 centimetres of tape. The length of the
photograph is 7 centimetres. What is the width of
the photograph?
𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 𝑜𝑓 𝑟𝑒𝑐𝑡𝑎𝑛𝑔𝑙𝑒 = 2(𝑙 + 𝑤)
24 = 2(7 + 𝑤)
24 = 14 + 2𝑤
2𝑤 = 24 − 14 = 10
𝑤 =
10
2
= 5 𝑐𝑚
The width of the photograph = 𝟓 𝒄𝒎
WORD PROBLEMS
• Jesse is making a circular picture frame. He
wants the diameter of the frame to be
28 𝑐𝑚. What length of material does he
need?
𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 𝑜𝑓 𝑐𝑖𝑟𝑐𝑙𝑒 = 𝑐𝑖𝑟𝑐𝑢𝑚𝑓𝑒𝑟𝑒𝑛𝑐𝑒 = 2𝜋𝑟
𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 𝑜𝑓 𝑓𝑟𝑎𝑚𝑒 = 2 ×
22
7
× 14 = 88
𝐿𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙 𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑑 = 𝟖𝟖 𝒄𝒎
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12. THE END
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