GoalFind the perimeter and the area of a rectangular pen and use the area to choose a pen for an animal.
New words
perimeter · the length of fence all the way round a penarea · the amount of flat space inside a shapesquare metre · the area of a square with sides of 1 metrepen · a fenced place where animals stay
Explanation
A farmer builds pens for animals. The fence goes around the outside, so its length is the perimeter, measured in metres. The space inside is the area, measured in square metres. Take a goat pen 4 m long and 3 m wide. Perimeter: 4 + 3 + 4 + 3 = 14 m. Area: 4 × 3 = 12 square metres, because there are 3 rows with 4 squares of 1 metre in each row. An animal needs enough space, so the farmer compares the area with a rule. In this lesson goats need an area of more than 24 square metres, chickens need less than 18 and sheep need more than 18 but less than 30.
Worked examples
A sheep pen is 7 m long and 4 m wide. Perimeter: 7 + 4 + 7 + 4 = 22 m. Area: 7 × 4 = 28 square metres. This is more than 18 and less than 30, so sheep can use it. Goats can use it too, because 28 is more than 24.
A chicken pen is 5 m long and 3 m wide. Perimeter: 5 + 3 + 5 + 3 = 16 m. Area: 5 × 3 = 15 square metres. Chickens need less than 18, so this pen is right for them.
Pen
Size
Area
Animals
A
6 m by 3 m
18
none
B
5 m by 5 m
25
goats, sheep
C
8 m by 4 m
32
goats
D
4 m by 4 m
16
chickens
Four pens: A is 6 m by 3 m, B is 5 m by 5 m, C is 8 m by 4 m and D is 4 m by 4 m. Their areas are 18, 25, 32 and 16 square metres. Goats (more than 24): B and C. Chickens (less than 18): D only, because 18 is not less than 18. Sheep (more than 18 and less than 30): B. Nobody can use pen A.
Class activity
Pen planner. Choose a space in the yard or on squared paper. Draw three different rectangular pens that each have an area of 12 square units. Write the perimeter of each one. Which pen needs the longest fence?
A pen is 8 m by 3 m. Which animals can use it by the rules in this lesson?
The area is 8 × 3 = 24 square metres. Goats need more than 24, so no. Chickens need less than 18, so no. Sheep need more than 18 and less than 30, so yes. Only sheep.
5
Seif says the perimeter of a 4 m by 3 m pen is 12 m, because 4 × 3 = 12. What is his mistake?
He found the area. The perimeter is 4 + 3 + 4 + 3 = 14 m. The area is 12 square metres.
