Chapter 10

Nickelle D

10.1 Area of Parallelograms and Trapezoids

Key Vocabulary

-base of a parallelogram

-height of a parallelogram

-bases of a trapezoid

-height of a trapezoid


Parallelograms


Formula to solve for area of Parallelogram

A=bh


What does A,b, and h mean?

A= area

b= base

h= height


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



Trapezoids


Formula to solve for the area of a Trapezoids

A=1/2(b1+b2)h


What do these letters mean when solving it?

A= area

b1= base one of the sides

b2= base two of one of the sides

h= height

1/2= one half


Important note when solving:

- the height of a trapezoid is perpendicular distances between the bases

How to Find the Area of a Parallelogram
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10.2 Area of Circles

Key Vocabulary

-area

-circle, radius, diameter, circumference

-pi


Circles


Formula to solve for the area of a circle

A=pi* r^2

A=d*pi


What Does pi, r, and d Mean?

pi= 3.14 (or a repeating decimal)

r= radius

d= diameter


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

Key Vocabulary

-solid, polyhedron, face

-prism

-pyramid

-cylinder

-cone

-sphere

-edge, vertex


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

Video for Lesson 22: Names of Three-Dimensional Figures

10.4 Surface Area of Prisms and Cylinders

Key Vocabulary

-net

-surface area


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?

SA= 2B+Ph


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?

SA=2B+Ch

SA=2*pi*r^2+2*pi*r*h

Use nets to represent three-dimensional figures and find surface area--Lesson 2 of 10 (CCSS: 6.G.4)

10.5 Surface Area of Pyramids and Cones

Key Vocabulary

- slant height


Surface Area of Pyramids


Formula for Solving the Surface Area of a Pyramid

SA= B+1/2Pl


Surface Area of a Cone


Formula for Solving the Surface Area of a Cone

SA= pi*r^2+pi*r*l



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

10.6 Volumes of Prisms and Cylinders

Key Vocabulary

-volume


Volume of a Prism

Formula for solving volume of a prism

V=Bh


Volume of a Cylinder


Formula for solving volume of a cylinder

V=Bh


Important Note when solving

-when labeling your final answer in volume, label it in units CUBED

10.7 Volumes of Pyramids and Cones

Key Vocabulary

-pyramid

-cone

-volume


Volume of a Pyramid


Formula for solving volume of a Pyramid

V=1/3*B*h


Volume of a Cone


Formula for solving volume of a Cone

V=1/3*B*h

or V=1/3*pi*r^2*h

12.5 Volume of Pyramids and Cones

Useful Formulas through out Chapter 10

A=bh - area for squares, rectangles, paralelogram

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)