Study P3 Mathematics Area and Perimeter 1 - Geniebook

# 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 Aquare 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?

1. A
2. B
3. C
4. 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?

1. A and B
2. A and C
3. B and C
4. C and D

(2) A and C

Question 7:

Look at the figures below.

1. Which figure has the greatest perimeter?

1. A
2. B
3. C
4. 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?

1. A and D
2. B and C
3. B and D
4. C and D

(1) A and D

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