measuring area & volume © 2013 meredith s. moody 1
TRANSCRIPT
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GeometryMeasuring area & volume
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Objective: You will be able to…
Find length, area, and volume measurements for basic polyhedrons
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Vocabulary
Length: For a 1-dimensional figure, the number of units from one end of the figure to the other
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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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Finding length: Example
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The crayon measures ~ 2.8 inchesThe pencil measures ~ 15.9 centimeters
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Finding length: You tryUsing the appropriate tool, measure the length of three different items in the room
Record your measurements using the appropriate units
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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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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)
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Area of rectangles: You tryUsing 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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Area of parallelogramsParallelograms are also
quadrilateralsYou can think of a parallelogram
as a transformed rectangleThe area of a parallelogram is
still the number of square units it covers
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Area of parallelogram: Example
Once your parallelogram becomes a rectangle, you can easily measure the area using the previous steps
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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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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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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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Area of trianglesThe height of a triangle is always
perpendicular to its base (90˚)
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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
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6cm
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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
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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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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
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Cube
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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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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: 9 x 6 = 54
Surface area = 54 ft²
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3 ft.
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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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Vocabulary
Volume: For a 3-dimensional figure, the number of cubic units that will fit inside the figure
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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)
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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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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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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
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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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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
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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!
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