# Chapter 10

## Formulas

Area of a Parallelogram A=bh

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

A=bh

A=12*6

A=36

## Area of a trapezoid

Here is a Practice Problem!! >>>

## Real life scenario

#1 you are building a garden and you want a certain area but you don't want it to be an ordinary rectangular garden you want it to be unique so you want it to be a trapezoid, and you have to find out how long each side should be.

#2 You want to put a book shelf in your room but you only want it to take up a certain area of your wall space, so you have to find the length and width for your book shelf.

## Formulas

Area of a circle- A=πr2

A=πr2

A=π*7*7

A= π*49

A=153.93804

See vocab sheet!

## real life scenario

you are working at a post office and you got the job of a box sorter. Your job was to sort boxes that were polyhedrons and boxes that were not polyhedrons. You need to know what a polyhedron is to accomplish this job!

## formulas

surface area of a prism- S=2B+Ph

Surface area of a cylinder- S=2B+2πrh

S=2B+Ph

S=90+108

198

## Surface area of a cylinder

S=2B+2πrh

S=226.194671058+339.292006588

S=565.486677646

## Real life scenario

You want to know how much paint you need to paint your room and your lamp pole.

## Formulas

Surface area of a pyramid- S=B+1/2Pl

Surface area of a cone- S=πr2+πrl

## Surface area of a pyramid

S=B+1/2Pl

S=256+1/2*64*17

S=256+544

S=800

**HINT** if the slant height is not there use the Pythagorean theorem

Surface Area Of A Pyramid

## Surface area of a cone

S=πr2+πrl

S=4π+24π

S=87.9645943005

Surface Area Of A Cone - VividMaths.com

## Real life scenario

#1You are making ice cream cones and you wan to make them with a certain diameter and height but you need to know how much dough you need minus the base.

#2 You are a window washer for the Luxor hotel, you need to know how many bottles of soap you need to buy to complete this task but first you have to find the surface area.

## Formulas

Volume of a prism- V=Bh

Volume of a cylinder- V=Bh

V=Bh

v=(bh1/2)h

v=(6*3*1/2)10

v=9*10

v=90

v=Bh

V=(πr2)h

v=(π*8*8)10

V=201.06*10

V=2010.6

## real life scenarios

#1 You want to add a bookshelf to your room, but you don't want it to take up too much room, so you have a certain volume in mind and you have to see if the bookshelf you want is small enough for your space.#2 You just got a circular hot tub and you want to see how much water it holds

## formulas

volume of a cone and a prism V=1/3Bh

V=1/3Bh

V=1/3(b*h)h

V=1/3(8*10)*6

V=1/3(80*6)

V=480*1/3

V=160

## real life scenario

#1 you wanted to put a small replica of a pyramid in your room but you only want it to take up so much room.

#2 you are eating an ice cream cone and you want to see how much ice cream is in your cone

## Extended chapter

Volume of a Sphere V=4/3πr3

Surface Area of a Sphere V=4πr2

## Formula Cheat sheet

Area of a parallelogram - A=bh

Area of a trapezoid- A=1/2h(b1+b2)

Area of a circle- A=πr2

Surface area of a pyramid- S=B+1/2Pl

Surface area of a cone- S=πr2+πrl

Surface area of a pyramid- S=B+1/2Pl

Surface area of a cone- S=πr2+πrl

volume of a cone and a prism V=1/3Bh

Volume of a prism- V=Bh

Volume of a cylinder- V=Bh

## Section 1

Base of a Parallelogram~ is the length of anyone of its sides

Height of a Parallelogram~The perpendicular distance between the base and the opposite side

Bases of a Trapezoid~ Its 2 parallel sides

Height of a trapezoid~ The perpendicular distance between the bases

## Section 2

Area- The number of square units covered by a figure

circle- the set of all points that are the same distance from a fixed point (radius)

radius- the distance from the center point to any edge of the circle

diameter- The length of a circle

Circumference- the distance around the circle

pi-π The ration of a circle's circumference to its diameter

## section 3

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

Polyhedron- A solid that is enclosed by polygons.

face- Polygons that form a polyhedron

Prism- A polyhedron that have 2 congruent bases that lie in parallel planes

Pyramid- A polyhedron that only has one base

Cylinder- a solid with 2 congruent circular bases that lie in parallel planes

Cone- a solid with one circular base

Sphere- a solid formed by all points in space that are the same distance from the center

## section 4

net- A 2D representational of a solid

Surface area- the sum of all areas of faces on a polyhedron

## section 5

Slant height- The height of a lateral face

## section 6

volume - the amount of space a solid occupies