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Geometry Formulas

Surface Area Volume

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! ?

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

TRIANGLES

You can tell the base and height of a triangle by

finding the right angle

CIRCLES

You must know the difference between RADIUS and

DIAMETER.

r d

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

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

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.

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

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!

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

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.

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)

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)

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

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.

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!

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

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

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