# Chapter 10

## 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

## 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)

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)