# 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

## 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

## 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

## 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

## 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)