chevron icon chevron icon chevron icon

Area And Perimeter

In this article, the learning objectives are: 

  1. Finding area on a square grid
  2. Finding perimeter on a square grid

Watch Our Video Lesson!

1. Finding area on a square grid

The area of a figure refers to the amount of space it occupies. 

Example 1: 

Solution:

Area of shaded figure \(= 9\) square units

Answer:

\(9\) square units

 

Question 1:

Look at the figure below.

The area of the shaded figure is __________ square units.

Solution: 

In the figure, there are 12 complete shaded squares and 2 shaded half squares.

Area of 2 shaded half squares \(=\) Area of 1 shaded square

Area of  the figure \(=\) 12 square units \(+\) 1 square unit
                                 \(=\) 13 square units

Answer:

13 square units

 

Question 2:

Look at the figure below.

What is the area of the shaded figure?

  1. 5 square units
  2. 6 square units
  3. 7 square units
  4. 4 square units

Solution:

In the figure, there are 6 complete shaded squares.

Area of  the shaded figure \(=\) 6 square units 

Answer:

(2) 6 square units

 

Question 3:

Look at the figure below.

What is the area of the shaded figure?

  1. 7 square units
  2. 8 square units
  3. 9 square units
  4. 10 square units

Solution: 

In the figure, there are 8 complete shaded squares and 2 shaded half squares.

Area of 2 shaded half squares \(=\) Area of 1 shaded square

Area of  the shaded figure \(=\) 8 square units \(+\) 1 square unit
                                                \(=\) 9 square units

Answer:

(3) 9 square units

 

Question 4:

Look at the figure below.

What is the area of the shaded figure?

  1. 12 square units
  2. 14 square units
  3. 15 square units
  4. 16 square units

Solution: 

In the figure, there are 12 complete shaded squares and 8 shaded half squares.

Area of 2 shaded half squares \(=\) Area of 1 shaded square

Area of 8 shaded half squares \(=\) Area of 4 shaded square

Area of the shaded figure \(=\) 12 square units + 4 square unit
                                              \(=\) 16 square units

Answer:

(4) 16 square units

Question 5:

Look at the figure below.

What is the area of the shaded figure?

Solution: Area of 1 small square\(\begin{align}\\[2ex] &= 2 \text{ cm } \times 2 \text{ cm }\\[2ex] &= 4 \text{ cm }^2 \end{align}\)

Number of shaded small squares \(= 9\)
Area of the shaded figure\(\begin{align}\\[2ex] &= 9 \times 4 \text{ cm}^2\\[2ex] &= 36 \text{ cm}^2 \end{align}\)

The area of the shaded figure is \(36 \text{ cm}^2\).

Answer:

\(36 \text{ cm}^2\)

Question 6:

Look at the figure below. 

  1. What is the area of 1 small square? 

Solution: Area of 1 small square\(\begin{align}\\[2ex] &= 2 \text{ cm } \times 2 \text{ cm }\\[2ex] &= 4 \text{ cm}^2 \end{align}\)

Answer:

\(4 \text{ cm}^2\)

  1. What is the area of the shaded figure?

Solution: 

Number of shaded squares \(= 15\)
Area of the shaded figure\(\begin{align}\\[2ex] &= 15 \times 4 \text{ cm}^2\\[2ex] &= 60 \text{ cm}^2 \end{align} \)

The area of the shaded figure is \(60 \text{ cm}^2\).

Answer:

\(60 \text{ cm}^2\)

Question 7:

Look at the figure below.

  1. What is the area of 1 small square? 

Solution: Area of 1 small square\(\begin{align}\\[2ex] &= 3 \text{ cm } \times 3 \text{ cm }\\[2ex] &= 9 \text{ cm}^2 \end{align} \)

Answer:

\(9 \text{ cm}^2\)

  1. What is the area of the shaded figure?

Solution: 

Number of shaded squares \(= 8\)
Area of the shaded figure\(\begin{align}\\[2ex] &= 8 \times 9 \text{ cm}^2\\[2ex] &= 72 \text{ cm}^2 \end{align} \)

The area of the shaded figure is \(72 \text{ cm}^2\).

Answer:

\(72 \text{ cm}^2\)

Question 8:

Look at the figure below.

  1. What is the area of 1 small square? 

Solution: Area of 1 square\(\begin{align}\\[2ex] &= 4 \text{ cm } \times 4 \text{ cm }\\[2ex] &= 16 \text{ cm}^2 \end{align}\)

Answer:

\(16 \text{ cm}^2\)

  1. What is the area of the shaded figure?

Solution: 

Number of shaded squares \(= 7 \)
Area of the shaded figure\(\begin{align}\\[2ex] &= 7 \times 16 \text{ cm}^2\\[2ex] &= 112 \text{ cm}^2 \end{align}\)

The area of the shaded figure is \(112 \text{ cm}^2\).

Answer:

\(112 \text{ cm}^2\)

2. Finding perimeter on a square grid

The perimeter of a figure refers to the outline of the figure. 

Example 1:

Look at the figure below:

Solution: 

Perimeter of figure \(= 16 \text{ m} \)

Answer:

\(16 \text{ m}\)

Question 1:

Look at the figure below.

What is the perimeter of the shaded figure?

Solution: 

To find the perimeter of the figure, we count the outline of the figure. 

The perimeter of the shaded figure is \(20 \text{ cm}\)

Answer:

\(20 \text{ cm}\)

Question 2:

Look at the figure below. 

What is the perimeter of the shaded figure?

  1. 8\(\text{ cm }\)
  2. 10\(\text{ cm }\)
  3. 12\(\text{ cm }\)
  4. 14\(\text{ cm }\)

Answer:

(3) \(12\text{ cm }\)

Question 3:

Look at the figure below:

What is the perimeter of the shaded figure?

  1. 20\(\text{ cm }\)
  2. 40\(\text{ cm }\)
  3. 52\(\text{ cm }\)
  4. 80\(\text{ cm }\)

Solution: Perimeter of the shaded figure\(\begin{align}\\[2ex] &= 20 \times 2 \text{ cm }\\[2ex] &= 40 \text{ cm } \end{align}\)

Answer:

(2) \(40 \text{ cm }\)

Question 4:

Look at the figure below. 

What is the perimeter of the shaded figure?

  1. 20\( \text{ cm }\)
  2. 100\( \text{ cm }\)
  3. 105\( \text{ cm }\)
  4. 500\( \text{ cm }\)

Solution: Perimeter of the figure\(\begin{align}\\[2ex] &= 20 \times 5 \text{ cm }\\[2ex] &= 100 \text{ cm } \end{align}\)

Answer:

(2) \(100 \text{ cm }\)

Question 5:

Look at the figures below.

  1. Figure __________ has the greatest area.
  2. Figure __________ has the greatest perimeter.

Solution:  

Figure A:

         Area \(= 6 \text{ cm}^2\)

Perimeter \(= 10 \text{ cm }\)

Figure B:

         Area \(= 3 \text{ cm}^2\)

Perimeter \(= 8 \text{ cm }\)

Figure C:

         Area \(= 5 \text{ cm}^2\)

Perimeter \(= 12 \text{ cm }\)

Figure D:

         Area \(= 4 \text{ cm}^2\)

Perimeter \(= 10 \text{ cm }\)

  1. Answer: A
  2. Answer:

Question 6:

Look at the figures below.

  1. Which figure has the greatest area?
  2. A
  3. B
  4. C
  5. D

Solution: Area of 1 small square\(\begin{align}\\[2ex] &= 2 \text{ cm } \times 2 \text{ cm } \\[2ex] &= 4 \text{ cm}^2 \end{align} \)

Figure A:

Number of squares \(= 4 \)
    Area of Figure A\(\begin{align}\\[2ex] &= 4 \times 4 \text{ cm}^2\\[2ex] &= 16 \text{ cm}^2 \end{align} \)

Figure B:

Number of squares \(= 5 \)
    Area of Figure B\(\begin{align}\\[2ex] &= 5 \times 4 \text{ cm}^2\\[2ex] &= 20 \text{ cm}^2 \end{align}\)

Figure C:

Number of squares \(= 4 \)
    Area of Figure C\(\begin{align}\\[2ex] &= 4 \times 4 \text{ cm}^2\\[2ex] &= 16 \text{ cm}^2 \end{align}\)

Figure D:

Number of squares \(= 6\)
    Area of Figure D\(\begin{align}\\[2ex] &= 6 \times 4 \text{ cm}^2\\[2ex] &= 24 \text{ cm}^2 \end{align}\)

Figure D has the greatest area.

Answer:

(4) D

  1. Which two figures have the same area?
  2. A and B
  3. A and C
  4. B and C
  5. C and D

Answer:

(2) A and C

Question 7:

Look at the figures below.

  1. Which figure has the greatest perimeter?
  2. A
  3. B
  4. C
  5. D

Solution: Perimeter of Figure A\(\begin{align}\\[2ex] &= 8 \times 2 \text{ cm }\\[2ex] &= 16 \text{ cm } \end{align}\)
Perimeter of Figure B\(\begin{align}\\[2ex] &= 12 \times 2 \text{ cm }\\[2ex] &= 24 \text{ cm } \end{align}\)
Perimeter of Figure C\(\begin{align}\\[2ex] &= 16 \times 2 \text{ cm }\\[2ex] &= 32 \text{ cm } \end{align}\)
Perimeter of Figure D\(\begin{align}\\[2ex] &= 8 \times 2 \text{ cm }\\[2ex] &= 16 \text{ cm } \end{align}\)

Figure C has the greatest area.

Answer:

(3) C

  1. Which two figures have the same perimeter?
  2. A and D
  3. B and C
  4. B and D
  5. C and D

Answer:

(1) A and D


 

Continue Learning
Volume Money
Mass Fractions
Addition And Subtraction Whole Numbers 1
Whole Numbers 3 Whole Numbers 6
Bar Graphs Angles
Multiplication And Division Length, Mass And Volume
Length Area And Perimeter
Parallel And Perpendicular Lines  

 

Resources - Academic Topics
icon expand icon collapse Primary
icon expand icon collapse Secondary
icon expand icon collapse
Book a free product demo
Suitable for primary & secondary
select dropdown icon
Our Education Consultants will get in touch with you to offer your child a complimentary Strength Analysis.
Book a free product demo
Suitable for primary & secondary
Claim your free demo today!
Claim your free demo today!
Arrow Down Arrow Down
Arrow Down Arrow Down
*By submitting your phone number, we have your permission to contact you regarding Geniebook. See our Privacy Policy.
Geniebook CTA Illustration Geniebook CTA Illustration
Turn your child's weaknesses into strengths
Geniebook CTA Illustration Geniebook CTA Illustration
Geniebook CTA Illustration
Turn your child's weaknesses into strengths
Get a free diagnostic report of your child’s strengths & weaknesses!
Arrow Down Arrow Down
Arrow Down Arrow Down
Error
Oops! Something went wrong.
Let’s refresh the page!
Error
Oops! Something went wrong.
Let’s refresh the page!
We got your request!
A consultant will be contacting you in the next few days to schedule a demo!
*By submitting your phone number, we have your permission to contact you regarding Geniebook. See our Privacy Policy.
Gain access to 300,000 questions aligned to MOE syllabus
Trusted by over 220,000 students.
Trusted by over 220,000 students.
Arrow Down Arrow Down
Arrow Down Arrow Down
Error
Oops! Something went wrong.
Let’s refresh the page!
Error
Oops! Something went wrong.
Let’s refresh the page!
We got your request!
A consultant will be contacting you in the next few days to schedule a demo!
*By submitting your phone number, we have your permission to contact you regarding Geniebook. See our Privacy Policy.
media logo
Geniebook CTA Illustration
Geniebook CTA Illustration
Geniebook CTA Illustration
Geniebook CTA Illustration Geniebook CTA Illustration
icon close
Default Wrong Input
Get instant access to
our educational content
Start practising and learning.
No Error
arrow down arrow down
No Error
*By submitting your phone number, we have
your permission to contact you regarding
Geniebook. See our Privacy Policy.
Success
Let’s get learning!
Download our educational
resources now.
icon close
Error
Error
Oops! Something went wrong.
Let’s refresh the page!