Geometry Formulas:

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Geometry Formulas
Surface Area Volume
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A formula is just a set of instructions. It
tells you exactly what to do! All you have to
do is look at the picture and identify the
parts. Substitute numbers for the variables and
do the math. Thats it! ?
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Lets start in the beginning Before you can do
surface area or volume, you have to know the
following formulas.
Rectangle A lw Triangle A ½ bh Circle A
p r² C pd
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TRIANGLES
You can tell the base and height of a triangle by
finding the right angle
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CIRCLES
You must know the difference between RADIUS and
DIAMETER.
r d
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Lets start with a rectangular prism.
Surface area can be done using the formula SA 2
lw 2 wl 2 lw OR Either method will gve
you the same answer.
you can find the area for each surface and add
them up.
Volume of a rectangular prism is V lwh
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Example
7 cm
4 cm
8 cm

Front/back 2(8)(4) 64 Left/right 2(4)(7)
56 Top/bottom 2(8)(7) 112 Add them up! SA
232 cm²
V lwh V 8(4)(7) V 224 cm³
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To find the surface area of a triangular prism
you need to be able to imagine that you can take
the prism apart like so
Notice there are TWO congruent triangles and
THREE rectangles. The rectangles may or may not
all be the same. Find each area, then add.
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Find the AREA of each SURFACE 1. Top or bottom
triangle A ½ bh A ½ (6)(6) A 18 2. The
two dark sides are the same. A lw A 6(9) A
54
Example 8mm 9mm 6 mm 6mm
3. The back rectangle is different A
lw A 8(9) A 72
ADD THEM ALL UP! 18 18 54 54 72 SA 216
mm²
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SURFACE AREA of a CYLINDER.
Imagine that you can open up a cylinder like so
You can see that the surface is made up of two
circles and a rectangle.
The length of the rectangle is the same as the
circumference of the circle!
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EXAMPLE Round to the nearest TENTH.
Top or bottom circle A pr² A p(3.1)² A
p(9.61) A 30.2
Rectangle C length C p d C p(6.2) C
19.5 Now the area A lw A 19.5(12) A 234
Now add 30.2 30.2 234 SA 294.4 in²
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There is also a formula to find surface area of a
cylinder. Some people find this way easier
SA 2prh 2pr² SA 2p(3.1)(12) 2p(3.1)² SA
2p (37.2) 2p(9.61) SA p(74.4) p(19.2) SA
233.7 60.4 SA 294.1 in²
The answers are REALLY close, but not exactly the
same. Thats because we rounded in the problem.
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Find the radius and height of the cylinder.
Then Plug and Chug Just plug in the numbers
then do the math. Remember the order of
operations and youre ready to go. The formula
tells you what to do!!!! 2prh 2pr² means
multiply 2(p)(r)(h) 2(p)(r)(r)
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Volume of Prisms or Cylinders You already know
how to find the volume of a rectangular prism V
lwh The new formulas you need are Triangular
Prism V (½ bh)(H) h the height of the
triangle and H the height of the
cylinder Cylinder V (pr²)(H)
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Volume of a Triangular Prism
We used this drawing for our surface area
example. Now we will find the volume. V (½
bh)(H) V ½(6)(6)(9) V 162 mm³
This is a right triangle, so the sides are also
the base and height.
Height of the prism
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Try one Can you see the triangular bases? V
(½ bh)(H) V (½)(12)(8)(18) V 864 cm³
Notice the prism is on its side. 18 cm is the
HEIGHT of the prism. Picture if you turned it
upward and you can see why its called height.
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Volume of a Cylinder
We used this drawing for our surface area
example. Now we will find the volume.
V (pr²)(H) V (p)(3.1²)(12) V
(p)(3.1)(3.1)(12) V 396.3 in³
optional step!
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Try one 10 m
d 8 m
V (pr²)(H) V (p)(4²)(10) V (p)(16)(10) V
502.7 m³
Since d 8, then r 4 r² 4² 4(4) 16
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Here are the formulas you will need to know A
lw SA 2prh 2pr² A ½ bh V (½ bh)(H) A
p r² V (pr²)(H) C pd and how to find the
surface area of a prism by adding up the areas of
all the surfaces