Geometry

Let’s Play with
Shapes…
In Geometry!

How do you find the area of a rectangle?
l
(length)
w (width)
The formula for Area of a
rectangle is A=l  w
(Area=length  width)
**For a square, all sides are
equal. So the formula will be A=
s  s = s2 (Area= side  side =
side2 )
s
s

How do you find the area of a
triangle?
The formula for Area of a
Triangle is A= ½ b  h (
Area= ½ base  height )
Practice!
In a triangle with base = 10 in, and height = 6 in, what is
the area?
A = ½  (10 in)  (6 in) = 30 in2 The area is 30 in2 .

trapazoid?
The formula for the Area of a
Trapazoid is A= ½  (b1 + b2 ) 
h ( Area= ½  ( base1 + base2 ) 
height )
Practice!
In a trapazoid with base1 = 5 m, base2 = 3 m, and height = 2 m, what is
the area?
Area = ½ (5 m + 3 m)  2 m = ½  8 m  2 m = 8 m2
The area is 8 m2 .

circle?
The formula for the Area of a
Circle is
A = π  r2 ( Area = π (pi)  radius2
)
*The radius is half of the diameter.
*The number pi can be replaced by
3.14 or 22/7 depending on what is
specified. Using one of these
replacements can alter your final
answer by a decimal.
*The circumference of a circle (like
the perimeter) is found by the
formula
C= 2  π  r

Let’s
Practice!
What is the area of a circle with radius = 10 in ?
A = 2 π r2
A = 2 (3.14) (10)2
A = 628 in2
The Area is 628 in2 .

CUBE
*Remember with a square, all
the sides are equal. The same
applies to a cube, which is
made up of squares on all
faces.
*Where two squares meet is
called an edge. The corners
are called vertices.
The formula for Volume of a
Cube is V= s3 ( Volume = side3
)s

CUBE
To find the Surface Area of a Cube, you need to find the sum
of all the faces. To do this you can use a net, or layout of the
faces. For a cube, you are adding the areas of 6 squares, or
multiplying the area of one square by 6.
Here is a formula for the Surface Area of a Cube, SA = 6 
s2
Practice!
For a cube with edge = 7 in, what is the surface area?
SA = 6  (7 in)2 The surface area is 294 in2 .

RECTANGULAR PRISM
*A rectangular prism is made up with
rectangles for each face.
Rectangular Prism is V= l  w  h (
Volume = length  width  height )
l (length)
w
(width)
h
(height)

RECTANGULAR PRISM
To find the Surface Area of a
Rectangular Prism, you can use
the net, and add together all the
faces.
You can also use the
formula:
SA= 2  ( w  h + l  w + l 
h)

Let’s
Practice
!
For a rectangular prism with length=5 in, width= 7 in and height = 3 in,
what is the surface area?
SA = 2 ( 7 in  3 in + 5 in  7 in + 5 in  3 in )
SA = 2 ( 21 in2 + 35 in2 + 15 in2 )
SA = 2 ( 71 in2 )
SA = 142 in2 The Surface Area is 142 in2 .
5 in
7 in
3 in

PYRAMIDS
*A pyramid is classified by the sides being
triangles. The type of pyramid is determined by the
base. A triangular pyramid has a base that is a
triangle. A square pyramid has a base that is a
square.

PYRAMID
*The height of the pyramid is the
perpendicular line from the apex (the
vertex where the sides of the triangles
meet at the top of the pyramid) to the
base.
*The slant height is the height of one
of the triangles on the side as if it were
a 2D triangle.
pyramid is V = 1/3  A  h
(Volume = 1/3  Area of the base 
height of the pyramid )
apex
base
height
slant
height

TRIANGULAR PYRAMID
The Surface Area of a triangular
pyramid can be found by using the
net, and adding the areas of all the
triangular faces.
It can also be found using the
formula SA = B + ½  P  l
( Surface Area = Base Area + ½ 
Perimeter of the base  slant
height )

Given a triangular pyramid with base sides = 10 cm and slant height =
5 cm, what is the surface area?
B = ½ bh P = 30 cm SA = 25√3 + ½
(30)(5)
B = ½ (10)(5√3) SA = 25√3 + 75 cm2
B = 25√3 cm2
The Surface Area is 25√3 + 75 cm2 .
10
cm
5 cm
Let’s
Practice!

SQUARE PYRAMID
The formula for Volume of a pyramid is
still V = 1/3  A  h
(Volume = 1/3  Area of the base  height
of the pyramid )
The formula for the
Surface Area of a Square Pyramid is
SA = 2  b  s + b2
( Surface Area = 2  side of the base 
slant height + side of the base2 )

TRIANGULAR PRISM
A triangular prism has two
triangles and three rectangles. It is
important to know if the triangles
are equilateral, which affects if the
rectangles are equal.
The formula for
Volume of a Triangular Prism
is
V = ½ (b  h)  l

TRIANGULAR PRISM
The formula for
Surface Area of a Triangular
Prism is SA = b  h + 2  l  s +
l  b
However for a triangular prism it
is easiest to find the surface
area using a net. Find the area
of each side and add them
together.

There are so many more
shapes to explore! Stay tuned
for more…
And Keep Practicing!

Geometry

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Geometry