# Chapter 10

## 10.1- areas of parallelograms and trapezoids

Vocabulary:

*Base of a Parallelogram: is the length of any one of it's sides

*Height of a Parallelogram: the perpendicular distance between the base and the opposite side

*Bases of a Trapezoid: are it's two parallel sides

*Height of a Trapezoid: the perpendicular distance between the bases

## How to solve for Areas of Parallelograms

A=bh-----------------Write out formula first

A=5x3----------------Then fill in the numbers that are the base and height

**LABELS!!**

## How to solve for Areas of Trapezoids

A=1/2(b1+b2)h--------Write out formula first

A=1/2(4+8)3------------Fill in correct numbers from the trapezoid

**LABELS!!**

## real life example

If you need to find the area of your roof of your house for a new roof, and it's shaped like a trapezoid, then you can use this formula to solve for the area.

## 10.2- Areas of Circles

Vocabulary:

*Area: the amount of surface the figure covers

*Circle: is the set of all points in a plane that are the same distance from a fixed point in the center

*Radius: the distance from the center to any point on the circle

*Diameter: is the distance across the circle that crosses through the center of the circle

*Circumference: the distance around the circle

*Pi: the non-repeating decimal that we use for finding the circumference and area of a circle

## video on how to find the circumference of a circle

Circumference of a Circle

## How to find the area of a circle

A= TTr2--------------Write out formula first

A=3.14(5)2----------Fill in the radius to solve,**remember to use 3.14 if told to**

A=78.5 units2-----Multiply to get your answer,**remember to round correctly if told to** **LABELS!!!**

## real life example for circumference

If you needed to find out how far the sprinkler sprayed around in a circle on your lawn. You would have to measure how far the sprinkler sprayed the water, that would be your radius, then put it in the formula C=2TTr, and there is the circumference of the lawn sprinkler's spray.

## 10.3 three-dimensional figures

Vocabulary:

*solid: a three dimensional figure that encloses a part of space

*polyhedron: a solid that is enclosed by polygons

*face: the polygons that form a polyhedron

*prism: is a polyhedron, that has two congruent bases that are parallel to each other.

*pyramid: is a polyhedron, that has one base, and the other faces are triangles

*cylinder: is NOT a polyhedron, and is a solid with two bases that are parallel to each other.

*cone: is a solid with one circular base

*sphere: is a solid formed by all points in space that are the same distance from a fixed point called the center.

*edge: the segments where faces of a polyhedron meet

*vertex: is a point where three or more edges meet.

## 10.4 surface areas of prisms and cylinders

Vocabulary:

*net: a two-dimensional pattern that forms a solid when it is folded

*surface area: is the sum of the area of it's faces.

## how to find the surface area of a prism

S=2B+Ph-----------------------------------Write out formula first

S=2(1/2x10x12)+(13+13+10)15----Then fill in the numbers to solve

S=660 units2----------------------------Multiply

**Labels!!**

**For a triangular prism remember to multiply by 1/2!**

## How to find the surface area of a cylinder

S=2TTr2+2TTrh--------------Write out formula first

S=2TT(4)2+2TT(4)(10.7)---Fill in numbers to solve

S=369.45 units2------------Multiply

**Labels!!**

## Real life example to use surface area

Let's say you have to wrap a present, and the gift is shaped as a prism. You can use this formula, S=2B+Ph, to give you your surface area of your gift you have to wrap.

## 10.5 surface areas of pyramids and cones

Vocabulary:

*slant height: or l of a regular pyramid is the height of a lateral face, which is, any face that isn't the base

## video on how to find the surface area of a pyramid

Surface Area of Pyramids

## how to find the surface area of a cone

S=TTr2+TTrl-----------------Write out the formula first

S=TT(4)2+TT(4)(9)---------Fill in the numbers to solve

S=163.4 units2-------------Multiply

**LABLES!!**

## real life example to use surface area

When a restaurant wants to sell ice cream with cones. They want to put a paper over the cone. They can find the surface area of the ice cream cone, using the formula S=TTr2+TTrl, then that's how much paper they need for each cone.

## 10.6 Volumes of Prisms and cylinders

Vocabulary:

*volume: is a measure of a solid's amount of space it takes up

## finding volumes of prisms

V=lwh----------------Write out formula first

V=12(8)(2)----------Fill in numbers to solve

V=192 units3-----Multiply

**LABELS!!**

** remember if a triangular pyramid divide by 1/2**

## finding volumes of cylinders

V=TTr2h--------------Write out formula first

V=TT(3)2(9)----------Fill in numbers to solve

V=81 units3--------Multiply

**LABELS!!**

## real life example for using volume

If a soup company wants to know how many fluid ounces can fit into one can of soup. Then they would use this formula, V=TTr2h, to find out how many fluid ounces can fit into one can of soup.

## 10.7 volumes of pyramids and cones

Vocabulary:

*pyramid: is a polyhedron, that has one base as any polyhedron, with the other faces as triangles

*cones: a solid with one circular base

*volume: is a measure of a solid and how much space it takes up

## video on how to find the volume of a pyramid

Volume of a Pyramid - MathHelp.com - Math Help

## finding the volume of a cone

V=1/3TTr2h----------------Write out formula first

V=1/3TT(6)2(12)----------Fill in numbers to solve

V=452.389 units3-------Multiply

**LABELS!!**

## real life example for using volume

If scientists wanted to find out how big the Ancient Egyptian pyramids were, they would have to use this formula, V=1/3Bh, to find out how big the pyramids are.

## 10.1 formulas

Area of a Parallelogram: A=bh

Area of a Trapezoid: A=1/2(b1+b2)h

## 10.2 formulas

Area of a Circle: A=TTr2

Circumference: C=TTd or C=2TTr

## 10.4 formulas

Surface Area of a Prism: S=2B+Ph Triangular: S=1/2(2)B+Ph

Surface Area of a Cylinder: S=2B+Ch OR S=2TTr2+ 2TTrh

## 10.5 formulas

Surface Area of a Pyramid: S=B+1/2Pl "B"=area of the base-lw

Surface Area of a Cone: S=TTr2+TTrl

## 10.6 formulas

Volume of a Rectangular Prism: V=Bh "B"=area of the base-lw

Volume of a Triangular Prism: V=Bh "B"=area of the base-1/2lw

Volume of a Cylinder: V=Bh "B"=area of the base-TTr2

## 10.7 formulas

Volume of a Pyramid: V=1/3Bh "B"=area of the base-lw

Volume of a Cone: V=1/3Bh "B"=area of the base-TTr2

Volume of a Sphere: V=4/3TTr3

Surface Area of a Sphere: A=4TTr2