Area And Perimeter

In this article, the learning objectives are: 

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

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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:

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

2. 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:

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

2. 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:

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

2. 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: C 

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

2. Which two figures have the same area?
3. A and B
4. A and C
5. B and C
6. 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

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

Answer:

(1) A and D