Math Skill: Perimeter and Area of Composite Figures
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Perimeter and Area of Composite Figures


For this topic, you need to know how to find the perimeter and area of rectangular shapes.
To review, see topics Perimeter and Compare Rectangle Area and Perimeter.

A composite figure is a figure that is made up of two or more basic shapes.
For example, putting two rectangles or a rectangle and a triangle together form composite figures.

 


Example 1: Perimeter and Area
Find the perimeter and area of each figure. Each unit is 1 cm. Label your answers in "cm".
For example, "6 cm" and "12 sq cm"

perimeter = area =

Perimeter
Add up the length of all the sides to get the perimeter.
Starting from point (1,6) and going clockwise, we get
  Perimeter = 1 cm + 3 cm + 3 cm + 2 cm + 4 cm + 5 cm
            = 18 cm

Area
Calculate the area of the composite figure by adding up the areas of the smaller shapes that make up the composite figure .
The figure can be divided in different ways. Here are two examples:
  
Area = Areas of the two rectangles      Area = Areas of the two rectangles
     = 3 sq cm + 8 sq cm                     = 5 sq cm + 6 sq cm
     = 11 sq cm                              = 11 sq cm


Example 2: Missing Sides

The figure is made up of rectangles.


To find the length of side A, look at the two rectangles that make up the figure.
Opposite sides of rectangles are the same length.
       5 cm = A + 3 cm
          A = 2 cm
 To find the length of side B, look at the two rectangles that make up the figure.
Opposite sides of rectangles are the same length.
       8 cm = B + 4 cm
          B = 4 cm

Complexity=2, Mode=align-grid

Find the perimeter and area of each figure. Each unit is 1 cm. Label your answers in "cm".
For example, "6 cm" and "12 sq cm"
1.   perimeter = area =
2.   perimeter = area =

Complexity=3, Mode=align-grid

Find the perimeter and area of each figure. Each unit is 1 cm. Label your answers in "cm".
For example, "6 cm" and "12 sq cm"
1.   perimeter = area =
2.   perimeter = area =

Complexity=2, Mode=jagged-grid

Find the perimeter and area of each figure. Each unit is 1 cm. Label your answers in "cm".
For example, "6 cm" and "12 sq cm"
1.   perimeter = area =
2.   perimeter = area =

Complexity=3, Mode=jagged-grid

Find the perimeter and area of each figure. Each unit is 1 cm. Label your answers in "cm".
For example, "6 cm" and "12 sq cm"
1.   perimeter = area =
2.   perimeter = area =

Complexity=2, Mode=align

Find the perimeter and area of each figure. Use labels.
All figures are made of rectangles.
1.   perimeter = area =
2.   perimeter = area =

Complexity=3, Mode=align

Find the perimeter and area of each figure. Use labels.
All figures are made of rectangles.
1.   perimeter = area =
2.   perimeter = area =

Answers

Complexity=2, Mode=align-grid

Find the perimeter and area of each figure. Each unit is 1 cm. Label your answers in "cm".
For example, "6 cm" and "12 sq cm"
#ProblemCorrect AnswerYour Answer
1 perimeter = area =
Solution
To get the perimeter, add up the lengths of all the sides.
  Perimeter = 1 cm + 2 cm + 1 cm + 4 cm + 2 cm + 2 cm = 12 cm

Looking at this figure, you can see that the figure is made up of rectangles.
To get the figure's area, add up the areas of the smaller rectangles.
  Area = (1 cm * 2 cm) + (1 cm * 4 cm) = 6 sq cm
#ProblemCorrect AnswerYour Answer
2 perimeter = area =
Solution
To get the perimeter, add up the lengths of all the sides.
  Perimeter = 3 cm + 1 cm + 2 cm + 5 cm + 5 cm + 4 cm = 20 cm

Looking at this figure, you can see that the figure is made up of rectangles.
To get the figure's area, add up the areas of the smaller rectangles.
  Area = (3 cm * 4 cm) + (2 cm * 5 cm) = 22 sq cm

Complexity=3, Mode=align-grid

Find the perimeter and area of each figure. Each unit is 1 cm. Label your answers in "cm".
For example, "6 cm" and "12 sq cm"
#ProblemCorrect AnswerYour Answer
1 perimeter = area =
Solution
To get the perimeter, add up the lengths of all the sides.
  Perimeter = 1 cm + 2 cm + 2 cm + 2 cm + 2 cm + 3 cm + 5 cm + 3 cm = 20 cm

Looking at this figure, you can see that the figure is made up of rectangles.
To get the figure's area, add up the areas of the smaller rectangles.
  Area = (1 cm * 3 cm) + (2 cm * 5 cm) + (2 cm * 3 cm) = 19 sq cm
#ProblemCorrect AnswerYour Answer
2 perimeter = area =
Solution
To get the perimeter, add up the lengths of all the sides.
  Perimeter = 3 cm + 1 cm + 1 cm + 1 cm + 3 cm + 3 cm + 7 cm + 3 cm = 22 cm

Looking at this figure, you can see that the figure is made up of rectangles.
To get the figure's area, add up the areas of the smaller rectangles.
  Area = (3 cm * 3 cm) + (1 cm * 2 cm) + (3 cm * 3 cm) = 20 sq cm

Complexity=2, Mode=jagged-grid

Find the perimeter and area of each figure. Each unit is 1 cm. Label your answers in "cm".
For example, "6 cm" and "12 sq cm"
#ProblemCorrect AnswerYour Answer
1 perimeter = area =
Solution
To get the perimeter, add up the lengths of all the sides.
  Perimeter = 3 cm + 3 cm + 1 cm + 4 cm + 1 cm + 1 cm + 3 cm + 2 cm = 18 cm

Looking at this figure, you can see that the figure is made up of rectangles.
To get the figure's area, add up the areas of the smaller rectangles.
  Area = (3 cm * 2 cm) + (1 cm * 4 cm) = 10 sq cm
#ProblemCorrect AnswerYour Answer
2 perimeter = area =
Solution
To get the perimeter, add up the lengths of all the sides.
  Perimeter = 2 cm + 2 cm + 1 cm + 3 cm + 1 cm + 1 cm + 2 cm + 2 cm = 14 cm

Looking at this figure, you can see that the figure is made up of rectangles.
To get the figure's area, add up the areas of the smaller rectangles.
  Area = (2 cm * 2 cm) + (1 cm * 3 cm) = 7 sq cm

Complexity=3, Mode=jagged-grid

Find the perimeter and area of each figure. Each unit is 1 cm. Label your answers in "cm".
For example, "6 cm" and "12 sq cm"
#ProblemCorrect AnswerYour Answer
1 perimeter = area =
Solution
To get the perimeter, add up the lengths of all the sides.
  Perimeter = 1 cm + 3 cm + 2 cm + 2 cm + 1 cm + 3 cm + 1 cm + 3 cm + 2 cm + 2 cm + 1 cm + 3 cm = 24 cm

Looking at this figure, you can see that the figure is made up of rectangles.
To get the figure's area, add up the areas of the smaller rectangles.
  Area = (1 cm * 3 cm) + (2 cm * 4 cm) + (1 cm * 3 cm) = 14 sq cm
#ProblemCorrect AnswerYour Answer
2 perimeter = area =
Solution
To get the perimeter, add up the lengths of all the sides.
  Perimeter = 1 cm + 2 cm + 1 cm + 1 cm + 1 cm + 3 cm + 1 cm + 1 cm + 1 cm + 1 cm + 1 cm + 2 cm = 16 cm

Looking at this figure, you can see that the figure is made up of rectangles.
To get the figure's area, add up the areas of the smaller rectangles.
  Area = (1 cm * 2 cm) + (1 cm * 3 cm) + (1 cm * 3 cm) = 8 sq cm

Complexity=2, Mode=align

Find the perimeter and area of each figure. Use labels.
All figures are made of rectangles.
#ProblemCorrect AnswerYour Answer
1 perimeter = area =
Solution
First calculate the lengths of the missing sides.

To get the perimeter, add up the lengths of all the sides.
  Perimeter = 1 in + 1 in + 2 in + 2 in + 3 in + 3 in = 12 in

Looking at this figure, you can see that the figure is made up of rectangles.
To get the figure's area, add up the areas of the smaller rectangles.
  Area = (1 in * 3 in) + (2 in * 2 in) = 7 sq in
#ProblemCorrect AnswerYour Answer
2 perimeter = area =
Solution
First calculate the lengths of the missing sides.

To get the perimeter, add up the lengths of all the sides.
  Perimeter = 1 in + 3 in + 1 in + 5 in + 2 in + 2 in = 14 in

Looking at this figure, you can see that the figure is made up of rectangles.
To get the figure's area, add up the areas of the smaller rectangles.
  Area = (1 in * 2 in) + (1 in * 5 in) = 7 sq in

Complexity=3, Mode=align

Find the perimeter and area of each figure. Use labels.
All figures are made of rectangles.
#ProblemCorrect AnswerYour Answer
1 perimeter = area =
Solution
First calculate the lengths of the missing sides.

To get the perimeter, add up the lengths of all the sides.
  Perimeter = 3 m + 1 m + 3 m + 1 m + 2 m + 4 m + 8 m + 4 m = 26 m

Looking at this figure, you can see that the figure is made up of rectangles.
To get the figure's area, add up the areas of the smaller rectangles.
  Area = (3 m * 4 m) + (3 m * 3 m) + (2 m * 4 m) = 29 sq m
#ProblemCorrect AnswerYour Answer
2 perimeter = area =
Solution
First calculate the lengths of the missing sides.

To get the perimeter, add up the lengths of all the sides.
  Perimeter = 2 ft + 2 ft + 2 ft + 1 ft + 3 ft + 3 ft + 7 ft + 2 ft = 22 ft

Looking at this figure, you can see that the figure is made up of rectangles.
To get the figure's area, add up the areas of the smaller rectangles.
  Area = (2 ft * 2 ft) + (2 ft * 4 ft) + (3 ft * 3 ft) = 21 sq ft
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