# Chapter 10

## Formulas

Area of a parallelogram- A=bh

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

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

Surface area of a cylinder- S=2B+Ch

Surface area of a pyramid- S=B+1/2P slant height

Volume of a prism- V=Bh

Volume of a cylinder- V=Bh

Volume of a pyramid- V=1/3Bh

Volume of a cone- V=1/3Bh

## 10.1 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 base and the opposite side

Bases of a trapezoid- its two parallel sides

Height of a trapezoid- perpendicular distance between the bases

Formula for area of a parallelogram- A=bh A- Area, b- Base, h- Height

Formula for area of a trapezoid- A=1/2(b1+b2)h A- Area, b1- One of the trapezoid bases, b2- The other base of the trapezoid, h- Height

Real life example and how to solve... You want to put a pool in your backyard, but you only have 300 square ft. to use. You aren't sure if you should build a trapezoid or parallelogram shaped pool. So you find out the measurements of the sides of the two different shaped pools lengths that you can buy. The parallelogram shaped pools height is 12 ft. and it's base is 24 ft. To find the area of this pool, you use the formula base times height, so 12*24= 288 ft. squared. Next, you find out the two lengths of the trapezoid shaped pool. It's height is 14 ft. one base is 20 ft., and the other is 15 ft. Now you would set up an equation using the formula for area of a trapezoid, A=1/2(15+20)14. Top down solve and you would get 245 ft. squared. You want the bigger pool so you would choose the rectangular shaped pool.

Area of a Trapezoid
Area of a Parallelogram

## 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

Diameter- The distance across the circle through the center

Circumference- The distance around a circle

Pi- The ratio of the circumference of a circle to its diameter

Formula for area of a circle- A=pi*r to the second power r-Radius

Real life example and how to solve... Your friend wants to put a well in his backyard and he asks you how the area of yours. You go out and measure the diameter of the circle, which is 6 ft. But for the formula you need the radius, so you divide the diameter by two. The formula would look like this- A=pi*3 to the second power. When you top down solve you get 84.8 ft squared.

## 10.3 Three-Dimensional Figures

Vocabulary:

Solid- three-dimensional figure that encloses a part of a space

Polyhedron- a solid that is enclosed by polygons. It has only flat surfaces.

Faces- the polygons that form a Polyhedron

Prism- a Polyhedron, it has two congruent bases that lie in parallel planes. The other faces are rectangles.

Pyramid- it is a Polyhedron, has one base. The other faces are triangles

Cylinder- a solid with two 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 a fixed point called the center

Real life example- in the picture below, you need to identify what the three-dimensional figure is and count its edges, vertices, and faces. You identify the solid as a rectangular prism and it has 6 vertices, 6 faces, and 12 faces.

Identifying Geometric Solids

## 10.4 Surface Areas of Prisms and Cylinders

Vocabulary:

Net- a two-dimensional pattern that forms a solid

Surface area- the sum of the areas of its faces

Formula for the surface area of a prism- S=2B+Ph S- Surface area, B- area of the base, P- base's perimeter

Formula for surface area of a cylinder- S=2B+Ch or S=2pi*r to the second power+2pi*rh

Real life example and how to solve- You are on a game show and you have been asked the \$1,000 question. You need to find the surface area of a cylinder and prism. You are given the dimensions of the cylinder and prism. The cylinder's base's radius is 4 cm and its height is 10.7 cm. You use the formula for the surface area of a cylinder and it looks like this.. S=2pi*4 to the second power+ 2pi*4*10.7. You top down solve and your answer is 369cm squared rounded. Next the dimensions of the prism are height- 12cm, and base- 10cm. You use the formula for the surface area of a prism and it looks like this... S=2*60+36*12. You top down solve and get 660cm squared. You got the answers correct and you win \$1,000.

## 10.5 Surface Areas of Pyramids and Cones

Vocabulary:

Slant height- height of a lateral face

Lateral face- any face that is not the base

Formula for surface area of a pyramid- S=B+1/2PL L- slant height

Formula for surface area of a cone- S=pi*r to the second power+pi*rL

Real life example and how to solve- Finding surface area of a pyramid in Egypt. Height- 100 Ft. base height- 20 Ft. base- 20 Ft. slant height- 50 Ft. S= (20*20)+1/2*80*50. S=400+1/2*4,000. S=400+2,000. S=2,400 Ft squared.

12.3 Surface Area of Pyramids and Cones 2nd Part

## 10.6 Volumes of Prisms and Cylinders

Vocabulary:

Volume- Solid measure of the amount of space it occupies

Formula for volume of a prism- V=Bh

Formula for volume of a cylinder- V=Bh or V=pi*r to the second power*h

Real life example- finding how much water box will hold. Height- 2 Ft. length- 2 Ft. width- 3 Ft. Equation would look like V=2*3*2. V=12 Ft. cubed.

## 10.7 Volumes of Pyramids and Cones

Vocabulary:

Pyramid- a solid, formed by polygons, that has one base. Base can be any polygon, and the other faces are triangles

Cone- a solid with one circular base

Volume- the amount of space the solid occupies

Formula for volume of a pyramid- V=1/3Bh

Formula for volume of a cone- V=1/3Bh or V=1/3pi*r to the second power*h

Real life example- Finding how much ice cream an ice cream cone will hold. Height- 4 in. Radius- 1 in. Equation would look like this- V=1/3pi*1*4 to the second power. V= 4.2 in squared.

## Spheres

Vocabulary:

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

Volume- the amount of space the solid occupies

Formula for volume of a sphere- S=4/3pi*r to the third power

Formula for surface area of a sphere- 4pi*r to the second power

Real life example- Finding surface area of a soccer ball. Radius- 3 in. Equation- S=4/3pi*3 to the second power. S= 12.6 in. Cubed.