# Chapter 10

## 10.1 Parallelograms and trapazoids

Parallelogram:

The base is the length of any one of the sides. The perpendicular distance between the base and oppisite side is the height

Trapezoid:

The bases of a trapezoid are its two parallel sides the perpendicular distance between the bases is the height

## 10.2 Circles

Radius- distancde from the center of the circle to an outer edge

Diameter- distance from one side of the circle to the other crossing through the middle

Circufrence- perimeter of a circle

## VOLUME (real life example)

You may need to find the volume of a ball to see how many will fit in a chest, you would also need to know the volume of the chest

## SURFACE AREA (real life example)

If you wanted to paint something like a locker you could find the surface area, buy the amount of paint that will be used so none is wasted

## 10.3 three dimensional figures

Solid- A 3-D figure that encloses a part of space

Polyhedron- A solid enclosed by polygons

Face- The polygons that form the polyhedron

Prism- Two congruent bases that lie in parallel planes the other faces are rectangles

Pyramid- One base and the other faces are triangles

Cylinder- Solid with two congruent circular bases that lie in parallel planes

Cone- Solid with one circular base

Sphere- Solid formed by points in space that are the same distance from the center

Edge- Where two faces meet

Vertex- Where three or more faces meet

( names of polyhedrons are determined by the shape of the base )

Since a circle is not a polygon because it hase no straight sides a cylinder is not a polyhedron

## 10.4 surface area of prisms and cylinders

Net- Two dimensional pattern that forms when a solid when it is folded

Surface area- The sum of the area of a polyhedrons faces

## 10.5 surface area of prisms and cones

Slant Height- The height of a lateral face (any face that is not a base)

Finding slat height => Use the pythagorean theorem

The heigt of a pyramid is the perpendicular distance between the vertex and base

## 10.6 volumes of prisms and cylinders

Volume- The measure of the amount of space it occupies

Volume is measured in cubic units, one cubic unit is the amount of space occupied by a cube that measures one unit on each side

the volume of a prism and a cylinder are very similar

## ALL FORMULAS

2-D

circle- A=π·r^2

trapezoid- A=0.5·(b1+b2)h

square- A=bh

parallelogram- A=bh

3-D

Sphere- V=4/3π·r^3

Prism- V=Bh (l·w·h)

Cone- V=1/3 Bh

Pyramid- V=1/3 Bh

Cylinder- V=π·r^2·h

SURFACE AREA

Prism- S=2B+Ph

Cone- S=π·r^2 + πrl

Pyramid- S=B+1/2·Pl

Sphere- S= 4πr^2

Cylinder-S=2B+Ch

l= slat height

C= circumfrence

B= area of the base

S= surface area

P= perimeter of the bse

h= height

b= base

s= side length of base