1. Measuring area & volume
Geometry
© 2013 Meredith S. Moody

2. Objective: You will be able to…
Find length, area, and volume measurements for basic polyhedrons
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3. Vocabulary
Length: For a 1-dimensional figure, the number of units from one end of the figure to the other
© 2013 Meredith S. Moody

4. Finding length Decide what tool is appropriate
Measure to the appropriate degree of accuracy
Record your measurement in the appropriate units
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5. Finding length: Example
The crayon measures ~ 2.8 inches
The pencil measures ~ 15.9 centimeters
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6. Finding length: You try
Using the appropriate tool, measure the length of three different items in the room
Record your measurements using the appropriate units
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7. Vocabulary
Area: For a 2-dimensional figure, the number of square units that figure covers
For quadrilaterals, counting these square units is easy
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8. Area of rectangles: Example
Rectangles are quadrilaterals
Here, a rectangle takes up 18 square units.
These units might be inches, centimeters, or even miles
Because it is rectangular, instead of counting, you can use multiplication (which is repeated addition)
© 2013 Meredith S. Moody

9. Area of rectangles: You try
Using the appropriate measurement tool, measure 2 different rectangles in the room
Record your measurements in square units
For example, your desktop might be 18 inches long and 20 inches wide, so 18 in. x 20 in. = 360 square inches
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10. Area of parallelograms
Parallelograms are also quadrilaterals
You can think of a parallelogram as a transformed rectangle
The area of a parallelogram is still the number of square units it covers
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11. Area of parallelogram: Example
Once your parallelogram becomes a rectangle, you can easily measure the area using the previous steps
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12. Area of parallelograms: You try
Find the area of the given parallelogram
Once you convert the parallelogram to a rectangle, it is easy to see that the shape takes up 40 square units, or 5 x 8
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13. Area of triangles
What is the relationship between a triangle and a square?
If you can find the area of a square, you can use it to find the area of a triangle
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14. Area of triangles
You can find the area (A) of a triangle more quickly by using a formula that is based on the rule that a triangle is half of a rectangle
A(triangle) = ½ (base x height)
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15. Area of triangles
The height of a triangle is always perpendicular to its base (90˚)
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16. Area of triangles: Example
What is the area of the pictured triangle?
The base = 8cm
The height = 5cm
8 x 5 = 40
40 ÷ 2 = 20
The area of this triangle = 20 cm²
6cm
© 2013 Meredith S. Moody

17. Area of triangles: You try!
What is the area of the given triangle?
base = 12 in.
height = 8 in.
12 x 8 = 96
96 ÷ 2 = 48
area = 48 in.²
© 2013 Meredith S. Moody

18. Vocabulary
Surface area: For a 3-dimensional figure, the sum of the surface area measurements of all the sides of the figure
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19. Surface area: Cubes
To find the surface area of a cube (3-dimensional quadrilateral), you must find the area of each surface and then add them together
Cube
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20. Surface area: Cubes
If all the surfaces are the same size (have the same area), you can use multiplication (repeated addition) to find the surface area more quickly
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21. Surface area: Cubes  You try!
Find the surface area of the given cube (all sides are equal lengths)
The area of each side is 3x3=9 square ft
There are 6 sides: x 6 = 54
Surface area = 54 ft²
3 ft.
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22. Surface area: Other solids
You can find the surface area of any 3-dimensional shape by measuring the area of all its surfaces and then finding the sum
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23. Vocabulary
Volume: For a 3-dimensional figure, the number of cubic units that will fit inside the figure
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24. Finding volume
For a 3-dimensional quadrilateral, find the length and width and height and multiply them all together
Your result will be cubic units (i.e. 9 cubic inches…in.³)
© 2013 Meredith S. Moody

25. Example: Volume What is the volume of the pictured solid?
The solid is 2 units wide, 3 units long, and 5 units high
We could count all the units, but multiplying is faster
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26. Finding volume: You try!
What is the volume of the pictured solid?
4cm x 3cm x 5cm = 60 cm³
The solid can hold 60 cubic centimeters
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27. You try! Measure the length of a pencil
Decide what measuring tool to use
ruler
Decide what units to use
Inches or centimeters
Measure to the appropriate degree of accuracy
© 2013 Meredith S. Moody

28. You try! Measure the area of a textbook cover Measure the length
Measure the width
Multiply them together
Report your measurement in square units
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29. You try! Find the volume of a rectangular prism Measure the length
Measure the width
Measure the height
Multiply them all together
Report your measurement in cubic units
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30. Class work
Work with a partner to measure 10 items in the classroom – you must have at least 1 length, 1 area, and 1 volume measurement
Remember to record your measurements in square or cubic units when appropriate!
© 2013 Meredith S. Moody