# Chapter 10

## Formulas

Area of a Parallelogram: A= b*h

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

Key:

A=Area

b= base of the shape

h= height of the shape

Area of a Trapezoid

## Real Life Scenario

You are building a garden and you want it in a shape of a trapezoid. You need to find out how big you can make so that it fits in the amount of space you have in your yard. You will have to take measurements for the size of your yard, then use the formula for area of a trapezoid to find the biggest size that will fit in your yard.

## Formulas

Area of a Circle: A= pi r squared

Key:

A= Area

Pi= 3.14....

## Vocabulary

Diameter: A line that crosses through the middle of a circle. The two end points of the line touch the edge of the circle

Radius: A line that goes to the middle of the circle, and reaches a midpoint.

Circumference: The distance around a circle. (the perimeter of a circle)

## Circumference

C= pi times diameter or 2pi times radius.

Key:

Pi= 3.14...

d= diameter

## Real Life Scenario

You have a job at a school to paint a circle for the playground. The school also wants you to mark the radius with a large dot. They tell you they want the diameter to be 8 feet. You will find the circumference by using the formula pi times diameter. You also know that the radius is 1/2 of the diameter.

## Vocabulary

Polyhedron: A solid that is enclosed by polygons, and has only flat surfaces.

Prism: A polyhedron that has two congruent bases that lie in parallel planes.

Pyramid: A polyhedron with one base. All the other faces are triangles.

Cylinder: A solid with two congruent circular bases.

Sphere: A 3-D circle. Like a ball.

Cone: A solid that has a circular base, and it comes to a vertex.

Vertex: When two or more edges meet and form a point.

Edge: Where two faces meet.

Face: A side of the solid.

## Real Life Scenario

You work for a company that makes soup cans. They tell you they want the can in a shape of a cylinder. This lesson would help you understand what a cylinder, and other three-dimensional shapes are.

## Formulas

Surface Area of a Prism: S= 2B+Ph

Key:

B = the area of the base
P = the perimeter of the base
h = the height of the prism

Surface Area of a Cylinder: S= 2*pi*r squared + 2*pi*r*h

Key:

h = height

## Vocabulary

Net: A two-dimensional pattern that forms a solid when it is folded
Surface Area: The sum of the areas faces

## Real Life Scenario

You are designing as cereal box, and you need to find to total surface area so you know how big to put on all the details. You will have to use the formula for the surface area of a prism. You will then take those measurements and decide how big you want the advertisements.

## Formulas

Surface Area of a Pyramid: S= B+1/2 Pl

Key:

B= the area of the base

P= Perimeter of the base

l= The slant height

Surface Area of a Cone: S= pi*r squared + pi*r*l

Key:

l=slant height

## Vocabulary

Slant Height: The height of a face

## Real Life Scenario

You are determined to find the surface area of a cone. You need to know the most possible cones you can stack, but they have to fit in the box the cones come in.

## Formulas

Volume of a Prism: V=B*h

Key:

B=area of the base

h=height

Volume of a Cylinder: B*h

Key:

B=are of the base= pi*r squared*h

## Vocabulary

Volume: the amount of space an object takes up in a place

## Real Life Scenario

You are designing a tissue box. The company says they want the box to hold 100 tissues. They give you the dimensions of each tissue. You have to come up with the volume of the box.

## Formulas

Volume of a Pyramid: V=1/3*B*h

Key:

B= area of the base

h= height

Volume of a Cone: V=1/3*B*h= 1/3 pi*r squared*h

## Real Life Scenario

You work at an ice cream stand. There are three different sizes of cones. You need to know the volume of the cones so you can find out how many scoops of ice cream fit in each cone.

## Volume of a Sphere

V=4/3*pi*r to the third
Volume of a Sphere

## All Formulas

Area of a Parallelogram: A=b*h
Area of a Trapezoid: A= 1/2(b1+b2)*h
Area of a Circle: A= pi*r squared
Surface Area of a Prism: S= 2B+Ph
Surface Area of a Cylinder: S= 2*pi*r squared + 2*pi*r*h
Surface Area of a Pyramid: S= B+1/2 Pl
Surface Area of a Cone: S= pi* r squared+ pi*r*l
Volume of a Prism: V= B*h
Volume of a Cylinder: V= pi*r squared*h
Volume of a Pyramid: V= 1/3 B*h
Volume of a Cone: V=1/3* B*h
Volume of a Sphere: V= 4/3 pi*r to the third