# Chapter 10

## Words to know

The base of a parallelogram is the length of any one of its sides.

The perpendicular distance between the base and the opposite side is the height of a parallelogram.

The base of a trapezoid are its two parallel sides.

The perpendicular distance between the bases is the height of a trapezoid.

b1-one of the two parallel lines on a trapezoid.

b2- one of the two parallel lines on a trapezoid.

## Example of a parallelogram

Question: Find the area of a parallelogram with a height of 12 cm and and a base of 16 cm

A=bh

A=12*16

A=192 cm squared

## Example of a Trapezoid

Question: Find the area of a trapezoid with a height of 6 inches a base of 8 inches and another base of 10 inches

A=1/2(b1+b2)h

A=1/2(8+10)6

A=9*6

A=54 inches squared

## Formulas

How to Find the Area of a Circle, Given a Radius or a Diameter

## Words to know

Radius- The distance from the edge of a circle to the center

Diameter- The distance from one edge to another on a circle crossing through the center point.

Circumference- The distance around a circle.

## Example of Area of a Circle

Question: Find the area of a circle with a radius of 10 in, use 3.14 for pi

A=pi*r^2

A=3.14*10^2

A=314 in squared

## Example of Circumference

Question: Find the circumference of a circle with a diameter of 10 inches

C=pi*2r

C=3.14*2*5

C=31.4 inches

C=pi*d

C= 3.14*10

C=31.4 inches

## Formulas

3D Shapes I Know (solid shapes song- including sphere, cylinder, cube, cone, and pyramid)

## Words to Know

A solid is a three-dimensional figure that encloses a part of space.

A polyhedron is a solid that is enclosed by polygons.

The polygons that form a polyhedron are called faces.

The segments where faces of a polygon meet are called.

A vertex is a point where three or more edges meet.

## Example

Question: Count the faces,edges, and vertices of rectangular prism.

Faces-6

Edges-12

Vertices-8

## Words to Know

A net is a two-dimensional that forms a solid when it is folded.

The surface area of a polyhedron is the sum of all the area of its faces.

## Example of Surface Area of a Prism

Question: Find the surface area of the rectangular prism above.

S=2B+Ph

S=2(bh)+Ph

S=2(9*4)+30*6

S=72+180

S+252 feet squared

## Example of Surface Area of a Cylinder

Question: Find the surface area of the cylinder above.

S=2B+Ch

S=2pi*r^2+2pi*r*h

S=2*3.14*2^2+3.14*2*2*5

S=87.92 centimeters squared

## Words to Know

The slant height of a regular pyramid is the height of a lateral face, that is, any faces that is not the base.

## Example of Surface Area of a Pyramid

Question: Find the total surface area of a pyramid with B;13 meters P;17 meters and l;11 meters

S=B+1/2Pl

S=13+1/2*17*11

S=13+93.5

S=106.5 meters squared

## Example of Surface Area of a Cone

Question:Find the surface area of the cone above.

S=pi*r^2+pi*rl

S=3.14*4^2+3.14*4*5

S=50.24+62.8

S=113.04 centimeters squared

## Words to Know

The volume of a solid is the measure of the amount of space it occupies.

## Example of Volume of a Prism

Question:Find the volume of a rectangular prism with a length of 7 inches, a width of 9 inches, and a height of 5 inches.

V=Bh

V=(7*9)5

V=315 inches cubed

## Example of Volume of a Cylinder

Question:Find the volume of a cylinder with a radius of 10 centimeters and a height of 20 centimeters.

V=Bh

V=(3.14*10)20

V=31.4*20

V=628 centimeters cubed

## Example of Volume of a Cone

Question: Find the volume of a cone with a radius of 3 inches and a height of 7 inches.

V=1/3Bh

V=1/3(3.14*3^2)7

V=1/3*28.26*7

V=65.94 inches cubed.

## Example of Volume of a Pyramid

Question:Find the volume of the pyramid above.

V=1/3Bh

V=1/3(10*8)6

V=1/3*80*6

V=160 inches cubed

A=bh

A=1/2(b1+b2)h

C=d*pi

C=2r*pi

A=pi*r^2

E=f+v-2

S=2B+Ph

S=2B+Ch

S=B+1/2Pl

S=4pi*r^2

V=Bh

V=1/3Bh

V=4/3pi*r^3

## What do the symbols mean in the formulas?

A= Area

b= base

h= height

B= area of the base

l= slant height

d= diameter

c= circumference

S= surface area

E=edges

f=faces

v= vertices

V=volume

b1= one of the parallel lines on a trapezoid

b2= one of the parallel lines on a trapezoid