PERIMETER BASICS
A rectangle has a length of 8 ft and a width of 3 ft.
What is the perimeter?
Answer: 22 ft
(8 + 3 + 8 + 3 OR 2 × (8 + 3))
Length = 6 ft
Width = 4 ft
Find the area.
Answer: 24 square feet
A garden is 15 ft long and 10 ft wide.
How much fencing is needed?
Answer: 50 ft
A classroom rug is 10 ft by 6 ft.
What is the area of the rug?
Answer: 60 sq ft
A student says the area of a 7 by 4 rectangle is 22.
What mistake did they make?
Answer: They added instead of multiplied.
Length = 12 cm
Width = 5 cm
Find the perimeter.
Answer: 34 cm
Length = 9 m
Width = 7 m
Find the area.
Answer: 63 square meters
A playground is 20 m long and 8 m wide.
The school wants to put a border around it.
How many meters of border are needed?
Answer: 56 meters
A farmer plants crops in a 14 m by 5 m field.
How many square meters of crops are planted?
Answer: 70 sq m
A student says the perimeter of a 9 by 3 rectangle is 27.
Explain the mistake.
Answer: They multiplied instead of adding all sides.
A rectangle has a perimeter of 30 inches.
Its length is 10 inches.
What is the width?
Answer: 5 inches
(2(10 + w) = 30 → 10 + w = 15 → w = 5)
A rectangle has an area of 40 square inches.
The width is 5 inches.
What is the length?
Answer: 8 inches
(5 × l = 40)
Maria walks around a rectangular park that is
25 ft long and 12 ft wide.
How far does she walk?
Answer: 74 ft
A wall is 12 ft long and 9 ft high.
How much area needs to be painted?
Answer: 108 sq ft
A student solved this problem:
“A garden is 8 ft long and 5 ft wide.
How much fencing is needed?”
The student answered:
40 square feet
What mistake did they make?
Answer:
They found the area (8 × 5 = 40) instead of the perimeter.
Fencing requires perimeter, not area.
True or False:
If you double the length of a rectangle, the perimeter doubles.
Answer: False
(Students must justify why.)
Two rectangles both have an area of 36 square units.
One is 6 × 6.
Name another possible dimension.
Possible answers: 9 × 4, 12 × 3, 18 × 2, etc.
A rectangular yard has a perimeter of 60 feet.
The length is 20 feet.
Find the width.
Answer: 10 feet
A rectangular playground covers 96 square meters.
The length is 12 meters.
What is the width?
Answer: 8 meters
A student says:
“The perimeter and area of a 10 by 4 rectangle are the same because both answers are 40.”
Explain why this is incorrect.
Answer:
Perimeter = 28 (10 + 4 + 10 + 4)
Area = 40 (10 × 4)
They are not the same and measure different things.
Perimeter is distance around.
Area is space inside.
A rectangle has a length that is 3 times its width.
The width is 6 inches.
What is the perimeter?
Answer:
Width = 6
Length = 18
Perimeter = 2(18 + 6) = 48 inches
A rectangle has a length of 14 feet.
Its width is half of its length.
What is the area?
Answer:
Width = 7 ft
Area = 14 × 7 = 98 square feet
A rectangular dog park has a perimeter of 84 meters.
The length is 26 meters.
What is the width?
Answer:
2(26 + w) = 84
26 + w = 42
w = 16 meters
A rectangular basketball court covers 144 square meters.
The width is 9 meters.
What is the length?
Answer:
9 × l = 144
l = 16 meters
A student forgot to label their answer.
Why is labeling important?
Answer: Units matter (feet vs square feet).