Download Area and Volume - mcs6

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Area—number of square units enclosed

Dimensions must all be the same unit

Altitude/Height—line perpendicular to the base
with triangles, parallelograms, or trapezoids
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Square/Rectangle
 Perimeter
(distance around)
P = 4 x S (square)
P=2L+2W
 Area
A = L x W (rectangle)
A = S x S (square)
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Circles
 Area
A = ∏ r ² or ∏ x r x r
 Circumference
C=∏xd
(1/2 diameter)
Radius
Diameter
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Parallelogram
A=bxh
Triangle
A=½bxh
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Trapezoid
A = ½ h(b1 + b2)
*or you can treat the trapezoid like a composite figure
by dividing it into simpler figure and finding the
area then adding the totals
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Circles
 Area -- A = ∏r²
 Circumference -- C = ∏d
or 2r∏
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3-D figures are also called space figures or
solids
Vertex-where lines meet at a point
Base-flat surface on the top and bottom of the
figure
Base edge-lines along the base
Lateral face-flat surface on sides of the figure
Lateral edge-lines along the sides of the figure
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Prism-2 parallel bases are congruent polygons
and lateral faces are rectangles
sides are always rectangles
base (can be any shape; same on both ends)
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Pyramid-1 polygon base the lateral faces are
triangles
vertex
sides are always triangles
base (can be any shape)
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Cylinder-2 parallel bases that are congruent
circles
base (always a circle)
sides are rounded
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Cone-1 circular base and 1 vertex
vertex
base (always a circle)
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Sphere-all points equal distance from center
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Net—pattern you can form into a space figure

Named for the bases

You must know what shape the bases and faces form
to be able to figure out a net
Cylinder
Triangular
Prism
Cube
Rectangular Pyramid
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Square Root– the inverse of squaring a number

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Symbol √
The square of an integer/number is a perfect square
On calculator: 2nd button then x² button then # then
enter
Irrational Number—decimal form of a number
that neither terminates or repeats

If an integer isn’t a perfect square, its square root is
irrational

The first 13 perfect squares are easy to memorize:
0² = 0
6² = 36
1² = 1
7²= 49
2² = 4
8² = 64
3² = 9
9² = 81
4² = 16
10²= 100
5² = 25
11² = 121
6² = 36
12²= 144
* a square is a number times itself
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Practice : (simplify & state whether it is rational or irrational)
1.) √64
2.) √100
3.) - √16
4.) - √121
5.) √27
6.) - √72
7.) - √50
8.) √2
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Volume—number of cubic units needed to fill
in a 3-D figure
Cubic unit—space occupied by a cube

This is why the units are cubed

Rectangular Prism or Cube
V=Lxwxh

Cylinder
V = ∏r2 x h
Volume of Triangular
V = (1/2 b x h) x h
Prism
Or V = b x h x h
Volume of a Cone or Pyramid
2
Pyramid
V = 1/3 ( L x w) x h
Or V = l x w x h
3
Cone
V = 1/3 (∏ r2) x h
Or V = ∏r² x h
3
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Surface Area (S.A.)—sum of the area of the
bases and the lateral sides of a space figure
Draw the figure
 Fill in all of the numbers for the edges



Find area of each face and add everything together
Sometimes it helps to draw a net figure then fill in
the numbers
Find each of the following areas:
Lxw
Lxh
wxh
Then add up all areas and multiply answer by 2
6
5
7
S.A. = l x w =
lxh=
wxh=
sum = ? x 2
answer = ?
*find area of circle then find area of rectangle
*formula for area of rectangle is (∏d x h)
Ex:
h= 11.5 cm
add
Area of the circle: A = ∏ r2
A=
A=?X2
Area of the rectangle : A = ∏ x d x h
A=
A=?
R = 3.5 cm
Total Area = ?
*
EX:
Area of Triangle: A = ½ b x h
A = ½ (6 x 4)
A=?X2
5 cm
6 cm
6 cm
5 cm
12cm
4 cm
* There
Area of Rectangle: A = l x w
A = 12 x 5
A=?X3
are 3 rectangle so multiply that area by 3
* There are 2 triangles so multiply that area by 2
Total Area = ?
Ex:
Area of Rectangle: A = l x w
A = 12 x 12
A=?
12 m
16 m
12 m
Area of the Triangle: A = ½ b x h
A = ½ (12 x 16)
A=?
There are 4 triangles so multiply the area of the triangle by 4.
Then add the area of the rectangle to the areas of the triangles.
Total Area = ?
Ex:
Area of the Triangle: A = ½ b x h
A = ½ (8 x 10)
10 m
14 cm
A=?
Area of the Circle: A = ∏ r2
A = 3.14 x 72
A=?
Add the areas of the circle and the triangle.
Total Area: ?
Ex:
S.A. = 4∏ r2
d = 5 in
S.A. = 4 x 3.14 x 2.52
S.A. = ?