088. Area of Rectangles and Metric Area Units
Learning Intentions
- To understand what the area of a two-dimensional shape is
- convert between metric areas (square millimetres, square centimetres, square metres, square kilometres, hectares)
- Solve the area of squares and other rectangles
Pre-requisite Summary
- Know that a two-dimensional shape is a flat shape with length and width
- Know that area measures the amount of surface covered inside a shape
- Know that area is measured in square units such as , , ,
- Know that a square unit means a by square of that unit
- Know that length and width must be in the same unit before calculating area
- Know that converting area units is different from converting length units
- Know that but
- Know that
- Know that
- Know that the area of a rectangle is found Use
Worked Examples
Worked Example 1
Decide whether each statement describes area.
a) The space inside a shape
b) The distance around a shape
c) The amount of surface covered
Worked Example 2
Convert the following metric areas.
a) to
b) to
c) to
Worked Example 3
Convert the following metric areas.
a) to
b) to
c) to
Worked Example 4
Find the area of a square with side length .
Worked Example 5
Find the area of a rectangle with length and width .
Worked Example 6
A rectangular playground is long and wide. Convert to the same unit and find the area.
Problems
Problem 1
Decide whether each statement describes area.
a) The space inside a shape
b) The length of the boundary
c) The amount of surface covered
Problem 2
Convert the following metric areas.
a) to
b) to
c) to
Problem 3
Convert the following metric areas.
a) to
b) to
c) to
Problem 4
Find the area of a square with side length .
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Problem 5
Find the area of a rectangle with length and width .
Problem 6
A rectangular garden is long and wide. Convert to the same unit and find the area.
Exercises
Understanding and Fluency
Exercise 1.
Decide whether each statement is about area.
a) The amount of space inside a shape
b) The distance around the outside of a shape
c) The number of square units covering a surface
Exercise 2.
Choose the most suitable unit for area.
a) The surface of a page
b) The floor area of a classroom
c) The area of a large farm
Exercise 3.
Convert the following.
a) to
b) to
c) to
Exercise 4.
Convert the following.
a) to
b) to
c) to
Exercise 5.
Convert the following.
a) to
b) to
c) to
Exercise 6.
Find the area of each square.
a) Side length
b) Side length
c) Side length
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Exercise 7.
Find the area of each rectangle.
a) Length , width
b) Length , width
c) Length , width
Exercise 8.
Find the area of each rectangle after converting units where needed.
a) by
b) by
c) by
Reasoning
Exercise 9.
Explain why area is measured in square units rather than ordinary length units.
Exercise 10.
A student says because . Explain the error.
Exercise 11.
Explain why the formula works for rectangles.
Exercise 12.
A student finds the area of a by rectangle by doing . Describe the mistake.
Problem-solving
Exercise 13.
A bedroom floor is long and wide. Find its area.
Exercise 14.
A square tile has side length . Find its area.
Exercise 15.
A rectangular sign is long and wide. Find its area in and in .
Exercise 16.
A farmer has a paddock with area . Write this area in .
Exercise 17.
A park covers . Write this area in hectares.
Exercise 18.
A rectangular vegetable patch is long and wide. How many square metres of soil does it cover?
Potential Misunderstandings
- A student may confuse area with perimeter and think area is the distance around a shape
- A student may forget that area describes the surface inside a two-dimensional shape
- A student may Use length units such as cm or m instead of square units such as or
- A student may think converting area units uses the same scale factor as converting length units
- A student may think instead of
- A student may multiply side lengths that are in different units without converting first
- A student may add the side lengths of a rectangle instead of multiplying them
- A student may forget that a square is a rectangle with equal side lengths, so its area is still found by multiplying two side lengths
- A student may omit units or write incorrect units in the final answer
Next: 089. Area of Parallelograms