# Chapter 10

## Chapter 10 Formula's

Trapezoid: A=1/2(b1+b2)h. b1 and b2 must be parallel.

Parallelogram: A=b*h

Triangle: 1/2b*h

3-D shapes: Surface Area

Pyramid: S=B +1/2Pl. S is surface area B is the area of the base, P is the perimeter of the base, and l is slant height.

Sphere:

3-D shapes: Volume

Prism: V= Bh. B is the area of the base and h is the height.

Cylinder: V=Bh

Cone: V=1/3*B*h

## Chapter 10 Section 1: Areas of Parallelograms and Trapezoids

Vocabulary

Base of a parallelogram- The length of any one of its sides

Height of a parallelogram- The perpendicular distance between the bases

Bases of a trapezoid- They are its 2 parallel sides

Height of a trapezoid- The perpendicular distance between the bases

Practice Problems

1. The picture below is of a parallelogram. We will be finding the area. The height is the perpendicular distance between the bases. Any side can be the base for a parallelogram, but for this problem the bottom makes the most sense. First, we write the formula Area=base*height. Next, we input the numbers in the problem. Area=5*2. The 5 is the base and 2 is the height. 2*5 is 10. The answer is 10 inches squared.

2. Your family is buying a new door. The dimensions of the door is 3 ft. by 8 ft. What is the area of the front of the door?

Real Life

This is relevant in life because if you try to organize rooms, you need to know the area of the room and the area of what you put in the room. That way you can see how much space you are using and only need to go to a store once if you are buy the object.

## Chapter 10 Section 2: Areas of a Circles

Vocab

Area- The amount of surface a figure covers

Circle- The set of all points in a plane that are the same distance from a fixed point

Radius- The distance from the center to any point on the circle

Diameter- The distance across the circle through the center, or twice the radius

Circumference- The distance around the circle

Pi- For every circle, the quotient of its circumference and its diameter is the same

Practice Problem (Use 3.14 for pi)

1. Find the area of this sign. The formula for a circle is pi*radius squared. The diameter of the sign is 8 in. First, pug in the numbers. A=3.14*4 squared. The radius is half the diameter. 3.14*4=12.56.

2. You are buying a clock for your bedroom wall. The area of the circle is 12.56 ft squared. What is the radius of the clock?

Real Life

You will need this in real life because if you buy a circular wall sign you need to know how much space is left and how it will look before you buy the object. Also, If you are planning to make the object you will need to know how much material to buy so you aren't left with lots of extra materials.

## Chapter 10 Section 3: Three-Dimensional Figures

Vocab

Solid- 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- A polyhedron that has two congruent bases with all other rectangular faces

Pyramid- A one based polyhedron with all other faces being triangles

Cylinder- A solid with two congruent circular bases

Cone- A solid with one base

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

Edge- The segments where faces of a polyhedron meet

Vertex- A point where three or more edges meet

Practice Questions

1. Classify the solid (ice cream cone). First we need should look at the shape of the base. The base is a circle. Next, we see if it has two bases or one. It has one base which makes it a cone.

2. Multiple Choice. What shape is the soup can?

A. Cone

B. Cylinder

C. Hexagonal Prism

D. Cube

Real Life

If you become a ice cream store owner you will use this to find how much ice cream you can put in it to still make a profit. Also, when you buy the cones you want to buy the most amount for the least price.

## Chapter 10 Section 4: Surface Areas of Prisms and Cylinders

Vocab

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

Surface Area- The sum of the areas of its faces

Practice Questions

1. Find the surface area of the prism given. B= 3 in squared, P= 6 in, h= 5 in. The formula for the area of prism is A=2B+Ph. First, we input the numbers. A=2(9) + 6*5. Then we solve. 2*9=18 and 5*6=30. 18 + 30 = 48 in squared.

2. Find the surface area of the combination puzzle below. The perimeter is 8 in., the area of the base is 7 in squared, and the height is 3 in. What is the surface area?

Real Life

You will use this in life to find the right sized cups. You want a cup that isn't huge, but still holds lots of liquid. Also, when you put it in the cabinet it needs to be able to get in and out with ease.

## Chapter 10 Section 5: Surface Areas of Pyramids and Cones

Vocab

Slant Height- The height of a lateral face, that is, any face other than the base

Practice Questions

1. Use 3.14 for pi. You and your friends are building a teepee. Find the amount of fabric needed. The amount of fabric or surface area can be found by 3.14*radius squared +3.14*radius*slant height. The height of the teepee will be 7 ft., the radius is 4 ft., and the slant height is 11 ft. When we pug in the formula for surface area it is S=3.14*16+3.14*4*11. 3.14*16=50.24. 3.14*4*11=138.16. 50.24+138.16=188.4 ft. squared.

2. Find the surface area of the pyramid toy. The area of the base is 5 in squared, the perimeter is 8.5 in, and the slant height is 6 in. What is the surface area of the toy?

Real Life

If you make water cups you want to use as little material as possible with it still holding enough liquid and still being functionable.

## Chapter 10 Section 6: Volumes of Prisms and Cylinders

Vocab

Volume- A measure of the amount it occupies

Practice Questions

1. Find the volume of the prism. The formula is V= B*h. B is area of the base and h is height. The area of the base is 10 ft. squared and the height is 4 ft. Now we pug in the numbers. V=10 squared* 4. 10 * 4 = 40 V= 40 ft cubed.

2. Find the volume of the prism. The height is 6 in and the area of the base is 50 in. What is the volume of the prism?

Real Life

You will need this in real life because when you buy storage containers. The container needs to hold enough stuff and still be the right size.

## Chapter 10 Section 7: Volumes of pyramids and cones

Vocab

Pyramid- A one based polyhedron with all other faces being triangles

Cone- A solid with one base

Volume- A measure of the amount it occupies

Practice Questions

1. Volume of a pyramid. B= 7in squared, h= 4in. The formula of a pyramid is 1/3*B*h. Pug in the numbers. V=7*3*1/3. 7*3=21. 21*1/3=7. V=7in cubed.

2. Find the volume of a pyramid (round to the nearest tenth if necessary. The height is 6.5 cm and the area of the base is 64 cm. What is the volume of the pyramid?

Real Life

If you work at a flower shop and you need to store flowers in a bag they fit best in a cone and you would need to find out how many flowers fit inside of the cone bag.