10.1 Area of Parallelograms and Trapezoids
-base of a parallelogram
-height of a parallelogram
-bases of a trapezoid
-height of a trapezoid
Formula to solve for area of Parallelogram
What does A,b, and h mean?
Important notes when solving:
- Don't let the slanted edges mix you up when trying to find height, it will always be the perpendicular distance between between the base and opposite side
Formula to solve for the area of a Trapezoids
What do these letters mean when solving it?
b1= base one of the sides
b2= base two of one of the sides
1/2= one half
Important note when solving:
- the height of a trapezoid is perpendicular distances between the bases
10.2 Area of Circles
-circle, radius, diameter, circumference
Formula to solve for the area of a circle
What Does pi, r, and d Mean?
pi= 3.14 (or a repeating decimal)
Important Notes When Solving
- when being told to use pi... read the directions. Check and see if you use 3.14 or the pi button if the question wants a specific answer.
10.3 Three-Dimensional Figures
-solid, polyhedron, face
Prisms, Pyramids, Cylinders, Cones, and Spheres
Classifying a 3-D figure
-Find the base of the solid
-count the number of edges, faces, and vertices
Why Find the Number of Faces, Edges and Vertices?
- finding the number of faces, edges, and vertices helps you classify the three-dimensional figure
Important Notes About Classifying
- always make sure that you find the base of the 3-D figure first
- if you cannot find out what the base is, count the number of edges, vertices, and faces
Real life examples
- a cardboard box
- pyramids in Egypt
- a soup can
10.4 Surface Area of Prisms and Cylinders
Surface Area of Prisms
What can I use to find Surface Area?
- you can draw a net of the 3-D figure as a net
What is a Net and how do you approach it?
- a 2-D pattern that forms a solid when folded
- when drawing a net of a 3-D figure, you lay out each face as if you were unfolding a cardboard box
What is the formula for solving?
Surface Area of Cylinders
What can I use to solve?
- as for a prism, you can use a net as well for cylinders
What is the formula for Solving Surface Area of a Cylinder?
10.5 Surface Area of Pyramids and Cones
- slant height
Surface Area of Pyramids
Formula for Solving the Surface Area of a Pyramid
Surface Area of a Cone
Formula for Solving the Surface Area of a Cone
What does l mean?
- l is the slant height of the pyramid
- l is the height of a lateral face, that is, any face that is not a base
Useful Formulas through out Chapter 10
A=pi*r² - area for a circle
A=(b1+b2)h*1/2 - area for a trapazoid
A=1/2b*h - area of a triangle
SA=2B+Ph -surface area of a prism
SA=2B+Ch or SA=2*pi*r²+2*pi*r*h -surface area of a cylinder
SA=B*1/2*P*l -surface area of a pyramid
SA=pi*r²+pi*r*l -surface area of a cone
V=Bh -volume of prisms, and cylinders
V=1/3*Bh -volume of pyramids and cones
C=2*pi*r -circumference of a circle (having the radius)
C=d*pi -circumference of a circle (having the diameter)