# Chapter 10

### Tess A.

## All Formulas

Area of Trapezoid: A= .5( b1+b2) h

Area of Circle: A=pi *r2

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

Surface area of a cylinder: S= 2B + Ch or 2*pi*r2 + 2*pi*r*h

Lateral surface area: 2*pi*r*h

Surface area of a pyramid: S= B+.5* Pl

Surface area of a cone: S=pi*r2 + pi*rl

volume of a prism: V= Bh

volume of a cylinder: V= Bh or V= pi*r2*h

volume of a pyramid: V= 1 third* Bh

volume of a cone: V= 1third* Bh or 1 third*pi*r2*h

volume of a sphere: V= four thirds* pi* r3

area of a rectangle: A=b*h

area of a square: A=s2

area of a triangle: A=.5*b*h

area of a circle: A=pi*r2

area of a trapezoid: A=.5*h*(b1+b2)

area of a parallelogram: A=b*h

area of a pentagon: A=.25 square root 5(5+2 square root 5) a2

slant height: square root r2 +h2

Surface area of a sphere: A=4*pi*r2

area of a hexagon: A= 3 square root 3 divided by 2 <-- fraction a2

## 10.1 Areas of Parallelograms and Trapezoids

Area of a Parallelogram: A= b*h

Area of a Trapezoid: A= .5(b1+b2)h

Vocab:

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

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

The base of a trapezoid are its two parallel sides

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

Practice:

Parallelogram,

h=3cm b=5cm

A=5*3

A=15cm squared

Real Life!

The Winslow House in River Forest, Illinois, was designed by Frank Lloyd Wright. The front part of the roof is a trapezoid. What is the area is b1=31ft b2=77ft and h=25ft?

Answer: 1,350ft squared

## 10.2 Areas of Circles

Area of a circle: A=pi*r2

Vocab:

A circle is the set of all points in a plane that are the same distance from a fixed point

Practice:

Circle

r=5

A=pi*5squared

A=78.53981634...

Real Life!

Jeff wants to put in a hot tub in his back yard. He needs to figure out how much space it will take up. Jeff said the diameter is 3ft. Calculate to find the area.

Answer: 7.068583471ft... or 8ft

## 10.4 Surface Area of Prisms and Cylinders

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

Surface area of a cylinder: 2B+Ch or 2*pi*r2 + 2*pi*r*h

Lateral surface area= 2*pi*r*h

Vocab:

(S) is surface area

(2B) is the sum of twice the area of the base

(Ph) is the product of the base's perimeter and the height

(Ch) is the product of the base's circumference and the height

A prism is a polyhedron that have two congruent bases that lie in parallel planes and the other faces are rectangles.

A cylinder is a solid with two congruent circular bases that lie in parallel planes

Practice:

Triangular Prism

B=.5*10*12cm

P=13+13+10cm

h=15cm

A+2(.5*10*12) + (13+13+10)15

A=660cm

## 10.5 Surface area of Pyramids and Cones

Surface area of a pyramid: S=B+.5*Pl

Surface area of a cone: S=pi*r2* + pi*r*l

Curved lateral surface of a cone: A= pi*r*l

Vocab:

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

(.5Pl) is one half of the product of the base perimeter and the slant height

Practice:

rectangular pyramid

B=27.7

P=24

l=6

S=B+.5*Pl

S=27.7+.5(24)(6)

S= about 99.7

Real Life!

Bob works at an ice cream shop. He decided to some extra chocolate to dip a cone in. Bob's not sure if he has enough chocolate so he want's to calculate the surface area of the cone. If the radius is 2in and the slant height is 4in, then what is the surface area?

Answer:37.69911184in squared or 37in squared

## 10.7 Volume of Pyramids and Cones

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

Volume of a cone: V=1/3*B*h or V=1/3*pi*r2*h

Vocab:

Pyramids are polyhedrons that have one base. The other faces are triangles

A cone is a solid with one circular base

Practice:

pyramid

B=30squared

h=15

V=1/3*B*h

V=1/3(30squared)(15)

=4500