# chapter 10

### Brook B

## 10.1- Area of a Parallelogram and trapezoid

__how to find the area of a parallelogram__

a= bh

the area of a parallelogram is the product of the base and the height

Example:

A= b write formula for area

= 8(10) substitute 8 for b and 10 for h

=80 multiply

__How to find the area of a trapezoid __

a= 1/2(b1+b2)h

the area of a trapezoid is one half the product of the sum of the bases and the height.

example:

a=1/2(b1+b2)h write formula for area

=1/2(31+77)25 substitute values for b1,b2 and h

=1350 multiply

## 10.2 Areas of Circles

__How to find the area of a circle__

a=(pi)r^2

the area of a circle is the product of pi and the square root of the radius

example:

a=(pi)r^2 write the formula

=3.14(5)^2 substitute 3.14 for pi and 5 for r

=78.5 evaluate using a calculate

## 10.3 Three-dimensional FIgures

10.3 Three-dimensional Figures

__How to classify 3D figures __

__How to count the faces, edges, and vertices __

__How to draw prisms and other 3D figures __

## 10.4 Surface areas of Prisms and Cylinders

__How to Find the surface area of a prism__

The surface area of a prism is the sum of twice the area of a base B and the product of the bases perimeter P and the height h.

S=2B+Ph

example:

S= 2B + Ph

=2(1/2*10*12) = (13+13+10)15

=660

__How to find the surface area of a cylinder__

the surface area of a cylinder is the sum of twice the area of the base B and the product

of the base's circumference C and the height h

S=2B+Ch= 2(pi)r^2+2(pi)rh

Example:

S=2(pi)r^2+(pi)rh write formula

=2(pi)4^2=2(pi)4*10.7 substitute 4 for r and 10.7 for h

=369.45 evaluate using calculator

## 10.5 Surface areas of pyramids and cones

__How to find the surface area of a pyramid__

The surface area of a regular pyramid is the sum of the area of the base B and one half the product of the base perimeter P and the slant height l

S= B+1/2*Pl

example:

B=27.7 find the area of the base

P=8+8+8=24 find the perimeter of the base (add up all the sides)

S=B+1/2Pl write the formula for the surface area of a pyramid

=27.7+1/2*24*6 substitute

=99.7 simplify

__How to find the surface of a cone__

the surface area of a cone is a the sum of the area of the circular base with radius r and the product of pi the radios r of the base and the slant height l

S=(pi)r^2+(pi)rl

example:

S= (pi)r^2= (pi)rl write formula for surface area of cone

= (pi)4^2+(pi)4*6 substitute 4 for r and 9 for l

=163.4 evaluate using calculator

## 10.6 volumes of prisms and cylinders

__How to find the volume of a prism__

the volume of a prism is the product of the area of the base B and the height h

V=Bh

example:

rectangular base

V=Bh

=lwh

=12*8*2

=192

triangular base

v=Bh

=1/2*4*3*10

=60

__How to find the volume of a cylinder __

The volume of a cylinder is the product of the area of a base B an d the height h

v=Bh

=(pi)r^2h

Example:

v=Bh write formula for volume

=(pi)r^2h write formula for a volume of a cylinder

=(Pi)3^2*9 substitute

=81(pi) simplify

=254.469 evaluate using a calculator

## How vegetables are canned

## 10.7 Volumes of Pyramids and cones

__How to find the volume of a Pyramid__

The volume V of a Pyramid is one third the product of the area of the base Base and the height h

V=1/3 Bh

example:

V=1/3Bh write the formula

=1/3*30^2*15 substitute for B and h

=4500 evaluate using a calculator

__How to find the volume of a cone__

The volume of a cone V is one third the product of the area of the base B and the height h

v==1/3*Bh=1/3

(pi)r^2h

example:

V=1/3(pi)r^2 write the formula

=1/3(pi)*6^2*12 substitute for r and h

=144(pi) simplify

=452.389 evaluate using calculator

## Formulas

area of a parallelogram: a=bh

area of a trapezoid: a=1/2(b1+b2)h

10.2

area of a circle: a=(pi)r^2

10.4

surface area of a prism: SA= 2B+Ph

surface area of a cylinder: SA=2B+Ch= 2(pi)r^2+2(pi)rh

10.5

surface area of a pyramid: SA= B+1/2*Pl

surface area of a cone: SA=(pi)r^2+(pi)rl

10.6

volume of a prism and a cylinder: V=Bh

rectangular prism B=lwh

Cylinder B=(pi)r^2

10.7

volume of a pyramid: V= 1/3Bh

volume of a cone: v==1/3*Bh=1/3

b= (pi)r^2h

## vocabulary

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

Height of a parallelogram: the perpendicular distance between the base and the opposite side

base of a trapezoid: are its two parallel sides

height of a trapezoid: perpendicular distance between the bases

10.3

soild: is a three-dimensional figure that encloses a part of space

polyhedron: is a solid that is enclosed by polygons

Faces: the polygons that form a polyhedron