Area

course Phy201

I hope this is alright I did it at VHCC before Accounting and

something didn't seem right so I copied it and e-mailed it home and

then to the work submit

The format is fine. We'll see about the work, but my prediction is that it will be good also.

001. Areas

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16:52:16

`q001. There are 11 questions and 7 summary questions in this

assignment.

What is the area of a rectangle whose dimensions are 4 m by 3

meters.

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RESPONSE -->

THe are of a triangle is length multiplied by width= 4m*3m = 12 sq

m

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16:53:04

A 4 m by 3 m rectangle can be divided into 3 rows of 4 squares, each

1

meter on a side. This makes 3 * 4 = 12 such squares. Each 1 meter

square has an area of 1 square meter, or 1 m^2. The total area of

the

rectangle is therefore 12 square meters, or 12 m^2.

The formula for the area of a rectangle is A = L * W, where L is the

length and W the width of the rectangle. Applying this formula to

the

present problem we obtain area A = L * W = 4 m * 3 m = (4 * 3) ( m *

m )

= 12 m^2.

Note the use of the unit m, standing for meters, in the entire

calculation. Note that m * m = m^2.

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RESPONSE -->

yes I see how to use better notation

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16:55:53

`q002. What is the area of a right triangle whose legs are 4.0

meters

and 3.0 meters?

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RESPONSE -->

The area of a rt. triangle is 1/2 base multiplied by the height or

legs

multiplied together divided by two or 4*3)(m*m)= 12 m^2

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16:56:20

A right triangle can be joined along its hypotenuse with another

identical right triangle to form a rectangle. In this case the

rectangle

would have dimensions 4.0 meters by 3.0 meters, and would be divided

by

any diagonal into two identical right triangles with legs of 4.0

meters

and 3.0 meters.

The rectangle will have area A = L * W = 4.0 m * 3.0 m = 12 m^2, as

explained in the preceding problem. Each of the two right

triangles,

since they are identical, will therefore have half this area, or 1/2

* 12

m^2 = 6.0 m^2.

The formula for the area of a right triangle with base b and

altitude h

is A = 1/2 * b * h.

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RESPONSE -->

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16:58:24

`q003. What is the area of a parallelogram whose base is 5.0 meters

and whose altitude is 2.0 meters?

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RESPONSE -->

area of a parallelogram is base multiplied by the altitude or( 5*2)

m*m= 10 m^2

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16:58:51

A parallelogram is easily rearranged into a rectangle by 'cutting

off'

the protruding end, turning that portion upside down and joining it

to

the other end. Hopefully you are familiar with this construction.

In

any case the resulting rectangle has sides equal to the base and the

altitude so its area is A = b * h.

The present rectangle has area A = 5.0 m * 2.0 m = 10 m^2.

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RESPONSE -->

yes i see

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17:00:32

`q004. What is the area of a triangle whose base is 5.0 cm and

whose

altitude is 2.0 cm?

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RESPONSE -->

Area of a triangle is 1/2 base * heigth or

(5*2)/2 (m*m)= 5m^2

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17:01:33

It is possible to join any triangle with an identical copy of itself

to

construct a parallelogram whose base and altitude are equal to the

base

and altitude of the triangle. The area of the parallelogram is A =

b

* h, so the area of each of the two identical triangles formed by

'cutting' the parallelogram about the approriate diagonal is A = 1/2

* b *

h. The area of the present triangle is therefore A = 1/2 * 5.0 cm *

2.0

cm = 1/2 * 10 cm^2 = 5.0 cm^2.

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RESPONSE -->

I need to look at the units closer

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17:03:22

`q005. What is the area of a trapezoid with a width of 4.0 km and

average altitude of 5.0 km?

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RESPONSE -->

THe area of a trapezoid is base * average height or

4 km *5km = 20km^2

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17:03:51

Any trapezoid can be reconstructed to form a rectangle whose width

is

equal to that of the trapezoid and whose altitude is equal to the

average of the two altitudes of the trapezoid. The area of the

rectangle,

and therefore the trapezoid, is therefore A = base * average

altitude.

In the present case this area is A = 4.0 km * 5.0 km = 20 km^2.

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RESPONSE -->

Yes I remembered that

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17:06:48

`q006. What is the area of a trapezoid whose width is 4 cm in whose

altitudes are 3.0 cm and 8.0 cm?

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RESPONSE -->

The area it the average of the alitiudes * the width or

(3cm+8cm)/2 *4=(11/2)*4=22cm^2

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17:07:08

The area is equal to the product of the width and the average

altitude.

Average altitude is (3 cm + 8 cm) / 2 = 5.5 cm so the area of the

trapezoid is A = 4 cm * 5.5 cm = 22 cm^2.

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RESPONSE -->

yes

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17:09:42

`q007. What is the area of a circle whose radius is 3.00 cm?

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RESPONSE -->

Area of a circle is pi *(r)^2 or 3.14*9=28.27cm^2

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17:11:17

The area of a circle is A = pi * r^2, where r is the radius. Thus

A = pi * (3 cm)^2 = 9 pi cm^2.

Note that the units are cm^2, since the cm unit is part r, which is

squared.

The expression 9 pi cm^2 is exact. Any decimal equivalent is an

approximation. Using the 3-significant-figure approximation pi =

3.14 we

find that the approximate area is A = 9 pi cm^2 = 9 * 3.14 cm^2 =

28.26

cm^2, which we round to 28.3 cm^2 to match the number of significant

figures in the given radius.

Be careful not to confuse the formula A = pi r^2, which gives area

in

square units, with the formula C = 2 pi r for the circumference.

The

latter gives a result which is in units of radius, rather than

square

units. Area is measured in square units; if you get an answer which

is

not in square units this tips you off to the fact that you've made

an

error somewhere.

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RESPONSE -->

yes

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17:14:53

`q008. What is the circumference of a circle whose radius is

exactly 3

cm?

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RESPONSE -->

you would use the numer of significate digits in pi or

pi*3.0000^2= 28.2743

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17:15:53

The circumference of this circle is

C = 2 pi r = 2 pi * 3 cm = 6 pi cm.

This is the exact area. An approximation to 3 significant figures

is 6

* 3.14 cm = 18.84 cm.

Note that circumference is measured in the same units as radius, in

this case cm, and not in cm^2. If your calculation gives you cm^2

then

you know you've done something wrong.

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RESPONSE -->

I need to include the units all the time

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17:17:18

`q009. What is the area of a circle whose diameter is exactly 12

meters?

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RESPONSE -->

This will be 3.14 *12m^2=452.16

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17:17:57

The area of a circle is A = pi r^2, where r is the radius. The

radius

of this circle is half the 12 m diameter, or 6 m. So the area is

A = pi ( 6 m )^2 = 36 pi m^2.

This result can be approximated to any desired accuracy by using a

sufficient number of significant figures in our approximation of pi.

For

example using the 5-significant-figure approximation pi = 3.1416 we

obtain A = 36 m^2 * 3.1416 = 113.09 m^2.

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RESPONSE -->

i'm getting tired I didn't even read the problem

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17:20:35

`q010. What is the area of a circle whose circumference is 14 `pi

meters?

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RESPONSE -->

Using the 2pi r formula you can see the radius is 7m so the area is

3.14 ( 7m)^2=153.86

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17:21:22

We know that A = pi r^2. We can find the area if we know the radius

r.

We therefore attempt to use the given information to find r.

We know that circumference and radius are related by C = 2 pi r.

Solving for r we obtain r = C / (2 pi). In this case we find that

r = 14 pi m / (2 pi) = (14/2) * (pi/pi) m = 7 * 1 m = 7 m.

We use this to find the area

A = pi * (7 m)^2 = 49 pi m^2.

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RESPONSE -->

I still are not including the units in my answer

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17:24:08

`q011. What is the radius of circle whose area is 78 square meters?

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RESPONSE -->

This should (78/pi)^-2 =4.98

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17:26:31

Knowing that A = pi r^2 we solve for r. We first divide both sides

by

pi to obtain A / pi = r^2. We then reverse the sides and take the

square root of both sides, obtaining r = sqrt( A / pi ).

Note that strictly speaking the solution to r^2 = A / pi is r =

+-sqrt(

A / pi ), meaning + sqrt( A / pi) or - sqrt(A / pi). However

knowing

that r and A are both positive quantities, we can reject the

negative

solution.

Now we substitute A = 78 m^2 to obtain

r = sqrt( 78 m^2 / pi) = sqrt(78 / pi) m.{}

Approximating this quantity to 2 significant figures we obtain r =

5.0

m.

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RESPONSE -->

Good explaination

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17:28:39

`q012. Summary Question 1: How do we visualize the area of a

rectangle?

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RESPONSE -->

lines drawn parellel to both sides at a distance in between = to the

base unit

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17:29:04

We visualize the rectangle being covered by rows of 1-unit squares.

We

multiply the number of squares in a row by the number of rows. So

the

area is A = L * W.

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RESPONSE -->

I should have but in the formula

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17:30:13

`q013. Summary Question 2: How do we visualize the area of a right

triangle?

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RESPONSE -->

Do the same as the rectangle and then draw a line across and this

shows

1/2 base * height

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17:30:34

We visualize two identical right triangles being joined along their

common hypotenuse to form a rectangle whose length is equal to the

base of

the triangle and whose width is equal to the altitude of the

triangle.

The area of the rectangle is b * h, so the area of each triangle is

1/2

* b * h.

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RESPONSE -->

yes

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17:31:57

`q014. Summary Question 3: How do we calculate the area of a

parallelogram?

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RESPONSE -->

It is the base * the height

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17:32:25

The area of a parallelogram is equal to the product of its base and

its

altitude. The altitude is measured perpendicular to the base.

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RESPONSE -->

yes should have used altitude

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17:33:13

`q015. Summary Question 4: How do we calculate the area of a

trapezoid?

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RESPONSE -->

we average the height and multiply by the width

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17:33:41

We think of the trapezoid being oriented so that its two parallel

sides

are vertical, and we multiply the average altitude by the width.

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RESPONSE -->

I still need to use altitude

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17:34:14

`q016. Summary Question 5: How do we calculate the area of a

circle?

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RESPONSE -->

This is PI * the radius squared

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17:34:27

We use the formula A = pi r^2, where r is the radius of the circle.

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RESPONSE -->

yes

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17:38:49

`q017. Summary Question 6: How do we calculate the circumference

of a

circle? How can we easily avoid confusing this formula with that

for

the area of the circle?

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RESPONSE -->

The circumference of the circle is 2 *PI* Radius of the circle

Remember

that if the 2 is first then you are lookingf at the circumference

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17:39:12

We use the formula C = 2 pi r. The formula for the area involves

r^2,

which will give us squared units of the radius. Circumference is

not

measured in squared units.

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RESPONSE -->

The square is good

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17:40:58

`q018. Explain how you have organized your knowledge of the

principles

illustrated by the exercises in this assignment.

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RESPONSE -->

I have been over these so many times in my life they are with me for

ever I hope

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17:41:02

This ends the first assignment.

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RESPONSE -->

"

As I figured, you're in good shape here.