Connecting Perimeters and Areas
When we work with shapes, there are two important measurements we can use- perimeter and area.
Perimeter
When we calculate the perimeter of a shape, we need to work out how far it is around the outside of that shape. Let's work through some examples now.
Area
When we calculate the area of a shape, we are looking at how much space is inside the shape. Let's look at how to calculate the area of our shapes.
How are area and perimeter related?
You may have noticed already that shapes with the same perimeter don't always have the same area, as shown in the rectangles below. Similarly, shapes with the same area don't always have the same perimeter.
Let's look more at the relationship between perimeter and area now.
Different rectangles can have the same perimeter. The rectangle with the largest area will be a square.
Worked examples
Question 1
All shapes with the same perimeter have the same area.
Is this statement true or false?
True
AFalse
B
question 2
Which of these rectangles has an area of $24$24 cm2 and a perimeter of $28$28 cm?
(Note: Diagrams are not to scale.)
$2$2 cm $12$12 cm A$4$4 cm $10$10 cm B$4$4 cm $5$5 cm C$3$3 cm $8$8 cm D
question 3
Look at the picture of the rectangle and answer the following questions.
What is the area of this rectangle?
What is the perimeter of this rectangle?
Identify all the shapes that have the same perimeter as this rectangle. (Shapes not to scale)
A
B
C
D