Perimeter
A square has sides that are each 7 inches long.
What is the perimeter?
A square has 4 equal sides:
7 × 4 = 28
Perimeter = 28 inches
Question: A rectangle is 8 meters long and 5 meters wide.
What is its area?
Answer: 40 square meters
Area = length × width
8 × 5 = 40
Question: A rectangle has an area of 45 square inches.
Its length is 9 inches.
What is its width?
Answer: 5 inches
45 ÷ 9 = 5
Question: A large rectangle measures 10 meters by 6 meters.
A smaller rectangle measuring 4 meters by 2 meters is removed from one corner.
What is the area of the remaining shape?
Answer: 52 square meters
Large rectangle:
10 × 6 = 60
Removed rectangle:
4 × 2 = 8
Remaining area:
60 − 8 = 52
Question: A student says:
“A square with sides of 6 inches has a perimeter of 12 inches.”
Is the student correct?
Answer: No.
Perimeter means adding all four sides:
6 + 6 + 6 + 6 = 24
The perimeter is 24 inches.
A rectangle is 9 meters long and 5 meters wide.
What is the perimeter?
Answer: 28 meters
Add all four sides:
9 + 5 + 9 + 5 = 28
Or:
2 × (9 + 5) = 28
Question: A square has sides that are each 9 feet long.
What is its area?
Answer: 81 square feet
9 × 9 = 81
Area = 81 square feet
Question: A square has a perimeter of 32 centimeters.
How long is each side?
Answer: 8 centimeters
A square has 4 equal sides:
32 ÷ 4 = 8
Question: A shape is made from two rectangles:
The rectangles do not overlap.
What is the total area?
Answer: 47 square units
Rectangle A:
8 × 4 = 32
Rectangle B:
5 × 3 = 15
Total:
32 + 15 = 47
A student says:
“A rectangle that is 8 meters long and 5 meters wide has an area of 26 square meters because 8 + 5 + 8 + 5 = 26.”
Is the student correct?
Answer: No.
The student found the perimeter incorrectly.
Perimeter:
8 + 5 + 8 + 5 = 26 meters
But area is:
8 × 5 = 40 square meters
Area = 40 square meters
Question: A rectangular garden is 14 feet long and 8 feet wide.
How much fencing is needed to go all the way around the garden?
Answer: 44 feet
14 + 8 + 14 + 8 = 44
The garden needs 44 feet of fencing.
Question: A classroom rug is 12 feet long and 6 feet wide.
What is the area of the rug?
Answer: 72 square feet
12 × 6 = 72
Question: A rectangle has a perimeter of 50 feet.
Its length is 15 feet.
What is its width?
Answer: 10 feet
The two lengths total:
15 + 15 = 30
Subtract from the perimeter:
50 − 30 = 20
The two widths total 20:
20 ÷ 2 = 10
Width = 10 feet
Question: A garden is made from a large rectangle measuring 12 meters by 8 meters.
A 4-meter by 3-meter flower bed takes up part of the garden.
How much area is left for grass?
Answer: 84 square meters
Garden:
12 × 8 = 96
Flower bed:
4 × 3 = 12
Grass:
96 − 12 = 84
Question: A student has a rectangular piece of paper that is 12 inches by 8 inches.
They want to cover it completely with squares that are 2 inches by 2 inches.
The student says:
“I can fit 24 squares.”
Are they correct?
Answer: Yes!
Along the length:
12 ÷ 2 = 6 squares
Along the width:
8 ÷ 2 = 4 squares
Total:
6 × 4 = 24 squares
So the student is correct.
Question: A rectangle has a perimeter of 36 centimeters.
Its length is 11 centimeters.
What is its width?
Answer: 7 centimeters
The perimeter is:
11 + 11 + width + width = 36
Subtract the two lengths:
36 − 22 = 14
The two widths total 14:
14 ÷ 2 = 7
Width = 7 cm
Question: A rectangular playground has an area of 96 square meters.
Its length is 12 meters.
What is its width?
Answer: 8 meters
Use:
Area = length × width
So:
96 = 12 × width
96 ÷ 12 = 8
Width = 8 meters
Question: A square has an area of 121 square inches.
How long is each side?
Answer: 11 inches
Because:
11 × 11 = 121
So each side is 11 inches.
Question: A rectangular patio is 10 feet by 7 feet.
A square section measuring 3 feet by 3 feet is added to one side.
What is the total area of the patio?
Answer: 79 square feet
Original patio:
10 × 7 = 70
Added section:
3 × 3 = 9
Total:
70 + 9 = 79
Question: Two students calculate the area of a rectangle that is 9 feet by 6 feet.
Who is correct? Explain.
Answer: Noah is correct.
Area is:
9 × 6 = 54
So the area is 54 square feet.
Maya added the dimensions instead of multiplying them.
Question: A shape is made from a rectangle with side lengths of 12 yards and 7 yards, but one 4-yard section of one side is removed.
The remaining outside edges have lengths:
12, 7, 8, 4, 4, 7 yards
What is the perimeter?
Answer: 42 yards
Add all the outside edges:
12 + 7 + 8 + 4 + 4 + 7 = 42
Perimeter = 42 yards
Question: A piece of wire is 48 inches long.
It is bent into a square.
What is the area of the square?
Answer: 144 square inches
The wire becomes the perimeter:
48 ÷ 4 = 12 inches per side
Now find the area:
12 × 12 = 144
Area = 144 square inches
Question: A rectangular poster has an area of 180 square inches.
The length is 15 inches.
What is the width?
Then find the poster's perimeter.
Answer: Width = 12 inches; Perimeter = 54 inches
First find the width:
180 ÷ 15 = 12
Now find the perimeter:
15 + 12 + 15 + 12 = 54
Final Answer:
Width = 12 inches
Perimeter = 54 inches
Question: A large square has an area of 144 square centimeters.
Three smaller squares, each with a side length of 4 centimeters, are attached along one side of the large square.
What is the total area of the figure?
Answer: 192 square centimeters
First find the side of the large square:
12 × 12 = 144
Each small square has area:
4 × 4 = 16
Three small squares:
16 × 3 = 48
Total:
144 + 48 = 192
Total area = 192 square centimeters
Question: A student records the following measurements for a rectangle:
Another student says the measurements cannot all be correct.
Is the second student correct?
Answer: No. The measurements are all correct.
Check the perimeter:
14 + 5 + 14 + 5 = 38 meters
Check the area:
14 × 5 = 70 square meters
So both measurements are correct.