091e. Area of Composite Shapes

Learning Intentions

• To understand what a composite shape is
• Identify simple shapes that make up a composite shape
• Solve the area of a composite shape

Pre-requisite Summary

• Know that a composite shape is a shape made by joining two or more simple shapes
• Know that common simple shapes include rectangles, squares, triangles and parallelograms
• Know that area measures the amount of surface inside a two-dimensional shape
• Know that area is measured in square units such as and
• Know how to find the area of a rectangle Use
• Know how to find the area of a triangle using
• Know how to find the area of a parallelogram using
• Know that the total area of a composite shape can be found by adding the areas of its parts

Worked Examples

Worked Example 1

A shape is made by joining two rectangles.

One rectangle measures by and the other measures by .

Find the total area.

Worked Example 2

An L-shaped figure can be split into two rectangles.

The first rectangle measures by and the second measures by .

Find the area of the composite shape.

Worked Example 3

A composite shape is made from a rectangle and a triangle.

The rectangle measures by .

The triangle has base and height .

Find the total area.

Worked Example 4

A composite shape is made from a parallelogram and a rectangle.

The parallelogram has base and height .

The rectangle measures by .

Find the total area.

Worked Example 5

A shape is made from three rectangles.

Their dimensions are , and .

Find the total area.

Worked Example 6

A garden bed is made from a rectangle and a triangle.

The rectangle is by , and the triangle has base and height .

Find the total area.

Problems

Problem 1

A shape is made by joining two rectangles.

One rectangle measures by and the other measures by .

Find the total area.

Problem 2

An L-shaped figure can be split into two rectangles.

The first rectangle measures by and the second measures by .

Find the area of the composite shape.

Problem 3

A composite shape is made from a rectangle and a triangle.

The rectangle measures by .

The triangle has base and height .

Find the total area.

Problem 4

A composite shape is made from a parallelogram and a rectangle.

The parallelogram has base and height .

The rectangle measures by .

Find the total area.

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Problem 5

A shape is made from three rectangles.

Their dimensions are , and .

Find the total area.

Problem 6

A garden bed is made from a rectangle and a triangle.

The rectangle is by , and the triangle has base and height .

Find the total area.

Exercises

Understanding and Fluency

Exercise 1.

Decide whether each shape is a composite shape.

a) A shape made from two joined rectangles

b) A single square

c) A shape made from a triangle and a rectangle

Exercise 2.

Identify the formula for the simple shapes that make up each composite shape.

a) An L-shape split into two rectangles

b) A house-shaped figure split into a rectangle and a triangle

c) A shape split into a parallelogram and a rectangle

Exercise 3.

Find the total area of each composite shape.

a) Two rectangles: and

b) Two rectangles: and

c) Two rectangles: and

Exercise 4.

Find the total area of each composite shape.

a) Rectangle and triangle with base , height

b) Rectangle and triangle with base , height

c) Rectangle and triangle with base , height

Exercise 5.

Find the total area of each composite shape.

a) Parallelogram with base and height , and rectangle

b) Parallelogram with base and height , and rectangle

c) Parallelogram with base and height , and rectangle

Exercise 6.

An L-shaped figure is split into two rectangles. Find the area.

a) and

b) and

c) and

Exercise 7.

A shape is made from three rectangles. Find the total area.

a) , ,

b) , ,

c) , ,

Exercise 8.

Find the total area of each composite shape.

a) Rectangle , triangle with base and height

b) Rectangle , triangle with base and height

c) Rectangle , triangle with base and height

Reasoning

Exercise 9.

Explain why splitting a composite shape into simple shapes helps to find its area.

Exercise 10.

A student says the area of a composite shape is found by adding all the side lengths. Explain why this is incorrect.

Exercise 11.

A composite shape is made from a rectangle and a triangle. Explain why the total area is found by adding the two areas, not multiplying them together.

Exercise 12.

A student splits the same composite shape in two different valid ways and gets the same total area. Explain why this happens.

Problem-solving

Exercise 13.

A patio is made from two rectangles. One is by and the other is by . Find the total area.

Exercise 14.

A sign is made from a rectangle with a triangle on top of base and height . Find the total area.

Exercise 15.

A floor plan shows an L-shaped room split into two rectangles measuring and . Find the area of the room.

Exercise 16.

A garden bed is made from a parallelogram with base and height and a rectangle . Find the total area.

Exercise 17.

A composite tile design is made from three rectangles with areas , and . Find the total area.

Exercise 18.

A playground section is made from a rectangle and a triangle with base and height . How many square metres does it cover?

Potential Misunderstandings

• A student may think a composite shape is a completely new type of shape rather than a shape made from simple shapes
• A student may not identify all of the simple shapes needed to split the figure correctly
• A student may confuse area with perimeter and add outside side lengths instead of areas
• A student may Use the wrong formula for one of the simple shapes
• A student may forget to divide by when finding the area of a triangle
• A student may use a slanted side instead of the perpendicular height
• A student may multiply or add measurements that belong to different parts of the shape incorrectly
• A student may find the areas of the parts correctly but then combine them incorrectly
• A student may omit square units in the final answer

Next: 092. Volume of Rectangular Prisms