# Chapter 10

## 10.1: Areas of Parallelograms and Trapezoids

**Vocab**

- Base of a parallelogram: The length of any side of the parallelogram can be used as the base.
- Height of a parallelogram: The perpendicular distance between the side whose length is the base and the opposite side.
- Base of a trapezoid: The lengths of the parallel sides of the trapezoid.
- Height of a trapezoid: The perpendicular distance between the bases of the trapezoid.

__Formulas__- Parallelogram: A=b*h Write formula for area.

A= 80 Multiply.

- Trapezoid: A=0.5(b1 + b2)h Write formula for a trapezoid.

A=0.5(108)25 Add b1 and b2 together.

A=54*25 Multiply 0.5*b.

A=1350 Multiply.

__Practice Problems__

- Find the area of a trapezoid with a height of 5 inches, a base 1 of 9 inches, and a base 2 of 18 inches.

- Find the area of a parallelogram that has a base of 10 feet and a height 21.5 feet.

__Real Life Situations__

- You need to design a garden in your lawn in a corner that you want the shape as a parallelogram. Along the wall you have 4 feet and 6 feet. You will need 24 feet of boarding. SInce you already have 2 of the 4 walls done, you just get 12 feet of wood boards to perfectly fit the garden in.

## 10.2: Areas of Circles

__Vocabulary:__- Area: The number of square units covered by a figure.
- Circle: The set of all points in a plane that are the same distance, called the radius, from a fixed point, called the center.
- Radius: The distance between the center and any point on the circle.
- Circumference: The distance around a circle.
- Diameter: The distance across the circle through the center.
- Pi: The ratio of the circumference of a circle to its diameter.

__Formulas:__- Area of a circle: A=pi*r^2

A=3.14(5)^2 Substitute 3.14 for pi and 5 for r

A=78.5 Evaluate using a calculator

- Finding the radius of a circle:

530.66=(3.14)r^2 Substitute 530.66 for A and 3.14 for pi.

169 = r^2 Divide each side by 3.14

√169 = r Take positive square root of each side.

13 = r Evaluate square root.

__Practice Problems:__

- Find the area of a circle with the diameter of 16 inches.

- FInd the area of a circle with a radius of 8 inches.

__Real Life Situations:__

Your boss at work needs you to design a new kind of rug. He asks you to make it with the radius of 8 feet.

## 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: A polygon that is a side of the polyhedron.
- Prism: A solid, formed by polygons, that has 2 congruent bases lying in parallel planes.
- Pyramid: A solid, formed by polygons, that has 1 base. This base can be any polygon, and the other faces are triangles.
- Cylinder: A solid with two congruent circular bases that lie in parallel plains.
- Cone: A solid with 1 circular base.
- Sphere: A solid formed by all points in space that are the same distance from a fixed point called the center.
- Edge: A line segment where 2 faces of the polyhedron meet.
- Vertex: A point at which three or more edges of a polyhedron meet.

__Formulas:__- None D:

__Practice Problems:__- How many edges does a pentagonal pyramid have? (10)
- Sketch a triangular prism.

__Real Life Situations:__- Your kids are getting into egyptian gods and pharaohs. He wants a pyramid toy. Instead of you buying one you decide to make one yourself. You need the amount of vertices and edges and faces. You make the pyramid.

## 10.4: Surface Area of Prisms and Cylinders

__Vocabulary:__- Net: A two-dimensional representation of a solid. This pattern forms a solid when it is folded.

- Surface Area: The sum of the areas of the faces of the polyhedron.

__Formulas:__- Surface Area of a prism: S=2B+Ph

P=perimeter of the base

S=2B+Ph

S=2(20*5)+(13+13+10+10)7

S=522

- Surface area of a cylinder: S=2B+Ch = 2(pi)r²+2(pi)rh

S=2(pi)4²+2(pi)4*10.7

S=pi*8+pi*85.6

S=25.12+268.784

S=369.45

__Practice Problems:__

- Find the surface area of a cylinder that has a radius of 6inches, a height of a 10 inches.

- Find the surface area of a prism with a rectangular base which has length of 10 inches, a height of 95 inches, and a hypotenuse of 95.5 inches, while the prism has a height of 65 inches.

__Real Life Situations:__

- Your boss at work needs you to paint the meeting room with a new design. You need to find out how much paint you need exactly to be able to tell him how much money you need.

## 10.5: Surface Areas of Pyramids and Cones

__Vocabulary:__- Slant Height: The height of any face that is not the base of a regular pyramid.

__Formulas:__- Surface area of a pyramid: S= B+0.5Pl

S=99.7

- Surface area of a cone: S=(pi)r^2+(pi)rl

S=(pi)16+(pi)36

S=183.4

- Getting the slant height of a Pyramid: A^2+B^2=C^2.
- Getting the slant height of a Cone: r^2+h^2=C^2

__Practice Problems: (See the picture before the video)____Real life situations: __

Your boss at work needs you to create a new type of ice cream cone that kids will like. It needs to be wider than 2 inches and it is as tall as 8 inches. What is the slant height of the ice cream cone?

## 10.6: Volumes of Prisms and Cylinders

__Vocabulary:__- volume: The amount of space the solid occupies.

__Formulas!:__- Volume of a prism: V=Bh (B is also l*w or the way to get the area of the solid's base)
- Volume of a Cylinder: V=Bh (B is (pi)r^2)

__Practice Problems:__- Look below again.

__Real Life Situations:__- Your boss wants to make a new tissue box that can only hold a certain amount of tissues. You need to find the volume of the tissue box to find out how many can fit.

## 10.7: Volumes of Pyramids and Cones

__Vocabulary:__- Pyramid: A solid, formed by polygons, that has 1 base. This base can be any polygon, and the other faces are triangles.
- Cone: A solid with 1 circular base.

__Formulas:__- Volume of a Pyramid: V=(1 third)Bh
- Volume of a Cone: V=(1 third)(pi)r^2h

__Practice Problems:__You know the drill already, me.

__Real Life Situation:__

Your boss needs you to find out how much ice cream an ice cream cone can hold. The radius is 1.5 inches and the height is 10 inches.