Area And Perimeter
In this article, the learning objectives are:
- Finding area on a square grid
- 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?
- 5 square units
- 6 square units
- 7 square units
- 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?
- 7 square units
- 8 square units
- 9 square units
- 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?
- 12 square units
- 14 square units
- 15 square units
- 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.
- 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:
\(4 \text{ cm}^2\)
- 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.
- 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:
\(9 \text{ cm}^2\)
- 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.
- 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:
\(16 \text{ cm}^2\)
- 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 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 \(= 16 \text{ m} \)
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?
- 8\(\text{ cm }\)
- 10\(\text{ cm }\)
- 12\(\text{ cm }\)
- 14\(\text{ cm }\)
Answer:
(3) \(12\text{ cm }\)
Question 3:
Look at the figure below:
What is the perimeter of the shaded figure?
- 20\(\text{ cm }\)
- 40\(\text{ cm }\)
- 52\(\text{ cm }\)
- 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?
- 20\( \text{ cm }\)
- 100\( \text{ cm }\)
- 105\( \text{ cm }\)
- 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.
- Figure __________ has the greatest area.
- 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 \(= 10 \text{ cm }\)
- Answer: A
- Answer: C
Question 6:
Look at the figures below.
- Which figure has the greatest area?
- A
- B
- C
- 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
- Which two figures have the same area?
- A and B
- A and C
- B and C
- C and D
Answer:
(2) A and C
Question 7:
Look at the figures below.
- Which figure has the greatest perimeter?
- A
- B
- C
- 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
- Which two figures have the same perimeter?
- A and D
- B and C
- B and D
- C and D
Answer:
(1) A and D
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