This document provides formulas and examples for calculating the areas and volumes of various geometric shapes. It introduces formulas for finding the area of rectangles, triangles, trapezoids, and circles. It then covers the volume and surface area formulas for cubes, rectangular prisms, pyramids including triangular and square pyramids, and triangular prisms. Examples are provided to demonstrate how to apply each formula to solve practice problems.

1. Let’s Play with
Shapes…
In Geometry!

2. 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

3. 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 .

4. How do you find the area of a
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 .

5. How do you find the area of a
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

6. 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 .

7. How
about some
3D shapes!

8. 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

9. 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 .

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

11. 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)

12. 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

13. 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.

14. 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.
The formula for Volume of a
pyramid is V = 1/3  A  h
(Volume = 1/3  Area of the base 
height of the pyramid )
apex
base
height
slant
height

15. 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 )

16. 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!

17. 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 )

18. 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

19. 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.

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