121r. Review Area of Shapes and Composite Figures

Learning Intentions

• To understand what the area of a two-dimensional shape is
• convert between different metric units of area, including hectares
• Solve the area of squares, rectangles, parallelograms and triangles
• To understand that the area of composite shapes can be found by adding or subtracting the area of more basic shapes

Pre-requisite Summary

• Know that two-dimensional shapes are flat shapes with length and width
• Understand that area measures the amount of surface inside a shape
• Know that area is measured in square units such as , , and
• Know basic metric length conversions such as and
• Be able to multiply whole numbers and decimals
• Understand that a square has all sides equal and a rectangle has opposite sides equal
• Know that a triangle can be seen as half of a matching parallelogram or rectangle
• Be able to split a complex shape into simpler shapes

Worked Examples

Worked Example 1

State what area means and Identify suitable units:

a) the space inside a book cover

b) the space inside a classroom floor

c) the space inside a farm

Worked Example 2

Convert between metric units of area:

a) to

b) to

c) to

Worked Example 3

Find the area:

a) a square with side length

b) a rectangle with length and width

c) a parallelogram with base and perpendicular height

Worked Example 4

Find the area of each triangle:

a) base , height

b) base , height

Worked Example 5

Find the area of a composite shape by addition:

a) a shape made from a rectangle and a rectangle

b) a shape made from two rectangles of areas and

Worked Example 6

Find the area of a composite shape by subtraction:

a) a rectangle with a rectangle removed

b) a square of side with a triangle of area removed

Problems

Problem 1

State what area means and identify suitable units:

a) the space inside a desktop

b) the space inside a sports field

c) the space inside a state park

Problem 2

Convert between metric units of area:

a) to

b) to

c) to

Problem 3

Find the area:

a) a square with side length

b) a rectangle with length and width

c) a parallelogram with base and perpendicular height

Problem 4

Find the area of each triangle:

a) base , height

b) base , height

Problem 5

Find the area of a composite shape by addition:

a) a shape made from a rectangle and a rectangle

b) a shape made from two rectangles of areas and

Problem 6

Find the area of a composite shape by subtraction:

a) a rectangle with a rectangle removed

b) a square of side with a triangle of area removed

Exercises

Understanding and Fluency

Exercise 1.

Complete each statement:

a) Area is the amount of what inside a shape

b) Area is measured in what units

c) The area of a rectangle is found by multiplying what by ______

Exercise 2.

Convert between metric units of area:

a) to

b) to

c) to

d) to

Exercise 3.

Convert between metric units of area:

a) to hectares

b) to

c) to

d) to

Exercise 4.

Find the area of each shape:

a) a square with side

b) a rectangle with length and width

c) a parallelogram with base and height

Exercise 5.

Find the area of each triangle:

a) base , height

b) base , height

c) base , height

Exercise 6.

Find the area of each shape:

a) a square with side

b) a rectangle with length and width

c) a parallelogram with base and height

Exercise 7.

Find the area of each composite shape by addition:

a) a rectangle joined to a rectangle

b) a rectangle joined to a rectangle

c) two rectangles of areas and

Exercise 8.

Find the area of each composite shape by subtraction:

a) an rectangle with a rectangle removed

b) a rectangle with a rectangle removed

c) a square of side with a rectangle of area removed

Reasoning

Exercise 9.

Explain why area is measured in square units instead of units such as cm or m.

Exercise 10.

A student says that the area of a rectangle with length and width is . Explain the mistake.

Exercise 11.

Noah says that the area of a parallelogram is found by multiplying the lengths of its sloping sides. Is he correct? Explain.

Exercise 12.

Explain why the area of a triangle is half the area of a rectangle or parallelogram with the same base and height.

Exercise 13.

A student finds the area of a composite shape by adding all the outside side lengths. Describe the error.

Problem-solving

Exercise 14.

A rectangular garden is long and wide. Find its area.

Exercise 15.

A triangular sail has base and height . Find its area.

Exercise 16.

A parallelogram has base and perpendicular height . Find its area.

Exercise 17.

A school field has area . Write this area in square metres.

Exercise 18.

A floor plan is made from a rectangle and an attached rectangle. Find the total area.

Exercise 19.

A rectangular block has a shed removed from one corner. Find the remaining area.

Potential Misunderstandings

• Students may confuse area with perimeter
• Students may Use one-dimensional units for area instead of square units
• Students may confuse length conversions with area conversions
• Students may think instead of
• Students may forget that
• Students may use the sloping side of a parallelogram instead of the perpendicular height
• Students may forget to divide by when finding the area of a triangle
• Students may add side lengths instead of multiplying dimensions when finding area
• Students may not split a composite shape into sensible basic shapes
• Students may add areas when subtraction is needed, or subtract areas when addition is needed

Next: 122. Area of Special Quadrilaterals