# Area And Perimeter

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

## 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

$9$ 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

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

(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

(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

(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 $36 \text{ cm}^2$.

$36 \text{ cm}^2$

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}

$4 \text{ cm}^2$

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 $60 \text{ cm}^2$.

$60 \text{ cm}^2$

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}

$9 \text{ cm}^2$

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 $72 \text{ cm}^2$.

$72 \text{ cm}^2$

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}

$16 \text{ cm}^2$

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 $112 \text{ cm}^2$.

$112 \text{ cm}^2$

## 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 $= 16 \text{ m}$

$16 \text{ m}$

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 $20 \text{ cm}$

$20 \text{ cm}$

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$\text{ cm }$

(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}

(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}

(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 $= 10 \text{ cm }$

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.

(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

(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.

(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

(1) A and D

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