Found 3 solutions by Theo, solver91311, JBarnum:
Answer by Theo(1348)
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You can
put this solution on YOUR website!use the formula for a trapezoid.
that formula is:
area =
b1 is the top base
b2 is the bottom base
a is the altitude (height) of the trapezoid.
attached reference helps you to see how this works.
http://www.mathopenref.com/trapezoidarea.html
how the formula was derived is a lot more complicated.
if you look at the picture of a trapezoid shown below, you will see that the trapezoid is composed of a rectangle and a triangle on each end.
The trapezoid in the picture is composed of the areas of 1+2+3.
2 is a rectangle.
1 and 3 are triangles.
if you complete a larger rectangle, then you will see that the area of this larger rectangle is composed of the areas of 1+2+3+4+5.
The area of 2 is made by the base b1 * the altitude (a).
The area of 1+2+3+4+5 is made by the base b2 * the altitude (a).
The formula for the area of the trapezoid is a*(b1+b2)/2 which is the same as:
(a*b1)/2 + (a*b2)/2
now a*b1 = the area called 2 which is the area of the smaller rectangle.
now also a*b2 = the area of (1+2+3+4+5) which is the area of the larger rectangle.
based on the previous 2 statements, the area of the trapezoid is equivalent to:
(2/2) + (1+2+3+4+5)/2
this is equivalent to:
the area of (2/2) + the area of (1/2) + (2/2) + (3/2) + (4/2) + (5/2)
now (2/2) + (2/2) = 2 so our formula becomes:
the area of 2 + the areas of (1/2) + (3/2) + (4/2) + (5/2)
we also know that the area of triangle 4 is equivalent to the area of triangle 1.
we also know that the area of triangle 5 is equivalent to the area of triangle 3.
This is because triangle 4 is congruent to triangle 1, and because triangle 5 is congruent to triangle 3. These triangles are congruent by SSS.
what this means is that we can substitute the area of triangle 1 for the area of triangle 4.
what this also means that we can substitute the area of triangle 3 for the area of triangle 5.
our formula of:
area of 2 + areas of (1/2) + (3/2) + (4/2) + (5/2)
can be made into:
area of 2 + areas of (1/2) + (1/2) + (3/2) + (3/2)
this is because 1 and 4 are equivalent, and 3 and 5 are equivalent.
since 1/2 + 1/2 = 1, and since 3/2 + 3/2 = 3, our formula becomes:
2 + 1 + 3.
if we reorder the terms, we get:
1 + 2 + 3 which is the area of our trapezoid.
by looking at each of the piece parts, we have determined that the area of the trapezoid given by the formula:
area = a*(b1+b2)/2
is equivalent to the formula:
area = (a*b1)/2 + (a*b2)/2 which is the area of the smaller rectangle divided by 2 plus the area of the larger rectangle divided by 2.
it's tricky, but it works.
if you can't deal with the complexity of the derivation, then just stick with the formula.
the formula for the area of a trapezoid is equal to (b1+b2)/2 * a.
Answer by solver91311(6137)
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You can
put this solution on YOUR website!
Probably the same way you would explain it to anyone else. The first thing you would need to do is to determine what the teacher listening to the explanation believes the word "trapezoid" to mean. If s/he is in the UK, s/he might believe the term "trapezoid" refers to a general quadrilateral having no parallel sides. In that case you would politely explain that there is no general method for finding the area of a trapezoid other than dividing the figure into two triangles, attempting to determine the areas of the two triangles, and then summing the two areas. On the other hand, particularly if your audience is from the US, I would say take the average of the measures of the two parallel sides, then multiply that result times the altitude of the trapezoid which is defined as the distance between the two parallel sides.
John

Answer by JBarnum(408)
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Question 272915: Hello,
I have been working on these math problems for a very long times, and I cannot figure out how to do them. Please help me out:
19.) Find the measures of an interior angle and an exterior angle of the indicated regular polygon.
Polygon: regular heptagon
Then number 25 is:
Find the value of n for each regular n-gon described
N-gon: each interior angle of the regular n-gon has a measure of 165 degrees
Thank you so much!
Answer by Alan3354(8338)
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You can
put this solution on YOUR website!19.) Find the measures of an interior angle and an exterior angle of the indicated regular polygon.
Polygon: regular heptagon
A heptagon has 7 sides.
The sum of the exterior angles always totals 360 degs
Ext angles = 360/7 =~ 51.43 degrees.
------------------------------------
The interior angles are 180 - Ext angle = 180 - (360/7) = 900/7 degs
=~ 128.57 degs
----------------
Then number 25 is:
Find the value of n for each regular n-gon described
N-gon: each interior angle of the regular n-gon has a measure of 165 degrees
-----------
The easiest way to do these is to find the Exterior angle first, = 180-165
Ext = 15 degs
The sum of Ext angles = 360
n = 360/15 = 24 sides and angles.
Question 272559: The height of a cylinder is six times its radius. Find a function that models the volume V of the cylinder in terms of its radius r.
Answer by ankor@dixie-net.com(7696)
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You can
put this solution on YOUR website!The height of a cylinder is six times its radius.
Find a function that models the volume V of the cylinder in terms of its radius r.
r = the radius,
6r = the height
:
V(r) =

:
V(r) =
Question 271031: I need help find in x and y in the following problem.
The shape is a parallelogram (rectangle) the right top corner has 3x in it. The bottom left corner has 63 degrees in it and the bottom right corner has 2y+ 7 degrees.
Answer by drk(1905)
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You can
put this solution on YOUR website!In a parallelogram adjacent angles are supplementary. From above we have
(i)

(ii)

we can solve for y in (ii) as
(iii)

then
(iv)

dividing, we get
(v)

Now we can solve for x in (i) as
(vi)

combine like terms to get
(vii)

subtract to get
(viii)

and divide to get
(ix)
Question 270882: Alexander and Judy are 32 miles apart on a calm lake paddling toward each other.Alexander paddles at 5 miles per hour, while Judy paddles at 8 miles per hour. How long will it take them to meet?
Answer by rfer(3386)
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Question 270186: The moon is about 384000 km from the earth and its path around the earth is nearly circular. find the circumference of the path described by the moon every month.
Answer by Alan3354(8338)
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Question 269365: True or False: The sum of the lengths of the diagonals of a rhombus is less than its perimeter.
Answer by edjones(4080)
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You can
put this solution on YOUR website!True
Special case square: Let each side = 1
each diagonal is sqrt(2) (Pythagoras)
2sqrt(2)=2.828 sum of the diagonals.
perimeter is 4
.
As one angle gets more acute and the other more obtuse the difference becomes even greater.
.
Ed
Question 268986: what is the greatest possible error of 17 inches
Answer by Alan3354(8338)
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Question 268898: if arc fbc is 300 degrees what is the measure of angle4
Answer by Alan3354(8338)
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Question 268966: what is the area of a rectangle if the diagnal is 8in and measures 30 degrees
Answer by drk(1905)
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You can
put this solution on YOUR website!The side opposite the 30 degree angle is 1/2 of the hypotenuse or 4. The side opposite the 60 degree angle is the side opposite the 30 x sqrt(3) , or in our case 4sqrt(3).
Area = length x width = 4 x 4sqrt(3) = 16sqrt(3)
Question 268315: describe each locus of point
1. in space, the locus of points equdistant from two parallel planes
2. in a plane, the locus of points 4 cm from the center of a circle whose radius id 5cm
3. in a plane, the locus of the centers of all circles with the radius 3 cm that are tangent to a given line L.
Answer by stanbon(29620)
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You can
put this solution on YOUR website!describe each locus of point
1. in space, the locus of points equdistant from two parallel planes
Ans: A plane midway between the given planes.
------------------------------------------------------
2. in a plane, the locus of points 4 cm from the center of a circle whose radius is 5cm
Ans: A cicle with center at the center of the given circle, with radius of 4 cm.
------------------------------------------------------
3. in a plane, the locus of the centers of all circles with the radius 3 cm that are tangent to a given line L.
Ans: Two lines parallel to the tangent line and 3 cm from it.
================================================================
Cheers,
Stan H.
Question 266339: If AC = 206 find the value of x. Then find AB and BC
Answer by Alan3354(8338)
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Question 264231: The perimeter of a triangle is 20 cm. If all the sides are tripled, the new perimeter will be _____ cm.
Answer by Alan3354(8338)
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Question 263328: Hi, I need help with this problem: Your older sister is getting married and to save money she is making her own cylinder shaped cake with three layers. Top layer: Radius= 3cm Height = 3 cm Middle Layer: Radius= 6cm Height = 4 cm Bottom layer: Radius = 10cm Height= 5cm If each tub of frosting costs $6.99 and a each tub of frosting covers 120 cm^2 of cake, figure out how much money your sister will have to spend on frosting.
Answer by nerdybill(2712)
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You can
put this solution on YOUR website!Your older sister is getting married and to save money she is making her own cylinder shaped cake with three layers. Top layer: Radius= 3cm Height = 3 cm Middle Layer: Radius= 6cm Height = 4 cm Bottom layer: Radius = 10cm Height= 5cm If each tub of frosting costs $6.99 and a each tub of frosting covers 120 cm^2 of cake, figure out how much money your sister will have to spend on frosting
.
Surface Area = Area of top +Area of the side
.
Surface Area = (Area of top) + (perimeter of top)* height
.
Surface Area = (pi r^2) + (2 pi r)* h
.
Top layer:
Surface Area = (3.14*3^2) + (2*3.14*3)* 3
Surface Area = (3.14*9) + (6*3.14)* 3
Surface Area = 84.78 cm^2
.
Middle layer:
Surface Area = (3.14*6^2) + (2*3.14*6)* 4
Surface Area = (3.14*36) + (12*3.14)* 4
Surface Area = 263.76 cm^2
.
Bottom layer:
Surface Area = (3.14*10^2) + (2*3.14*10)* 5
Surface Area = (3.14*100) + (20*3.14)* 5
Surface Area = 628 cm^2
.
Total area = 976.54 cm^2
.
Deciding how many tubs:
976.54/120 = 8.14 tubs
.
Since you can't buy a partial tub, you must buy the next whole number up:
9 tubs of frosting
.
Total cost:
9 * 6.99 = $62.91
Question 263006: A couple is making their own wedding cake that has 3 layers. The Top layer: Diameter: 6cm Height: 3cm .... Middle Layer: Diameter 12 cm Height: 4cm...... Bottom Layer: Diameter: 20cm Height: 5cm . The couple wants to know how much to spend on frosting. If each tub of frosting costs $6.99 a tub and each tub of frosting covers 120cm^2 Figure out how much money the couple will have to spend on frosting. ( when calculating the surface area of the cylinders/layers, don't include the bottom base of each layer/cylinder because the bottom base will not get frosting. ) SA of cylinder = 2*(pi)*R*H + 2*(pi)*R^2
Answer by richwmiller(3971)
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put this solution on YOUR website!That is the wrong formula for surface area because we will never be covering the bottom of the cake and we also need to subtract the area of the layer above.
pi*r^2
3.14*6^2
pi*r^2
3.14*12^2
sa=2*pi*r*h+pi*r^2
sa=2*3.14*20*5+3.14*20^2
sa=2*3.14*12*4+3.14*12^2
sa=2*3.14*6*3+3.14*6^2
add those three and subtract
both
3.14*6^2
3.14*12^2
so we just add
sa=2*3.14*20*5+3.14*20^2
sa=2*3.14*12*4
sa=2*3.14*6*3
Question 261897: how do i determine which angle has the greatest measure ?
Answer by Alan3354(8338)
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Question 244366: A fifty pound play sand will fill approximately1/2 cubit foot I want to fill it
3/4 high how many whole bags of sand will I need to purchase?
Answer by Alan3354(8338)
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Question 259590: Carlos leaves Los Angeles on a cross-country car trip at 8:00 a.m. He averages 50 miles per hour. Juanita plans to take exactly the same route, but does not leave until 9:00 a.m. She averages 60 miles per hour. Develop a diagram or table to determine at what time Juanita will pass Carlos.
Answer by Alan3354(8338)
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You can
put this solution on YOUR website!In 1 hour, from 0800 to 0900, Carlos has gone 50 miles.
Juanita gains on him at 10 mph (60-50).
She will pass him in 5 hours (50/10).
0900 + 500 = 1400, or 2 PM.
--------------
I see no need for a diagram or a table.
Question 259387: What is the y-intercept of the plane whose equation is 4x + 5y + z = 20?
Found 2 solutions by Edwin McCravy, richwmiller:
Answer by Edwin McCravy(3640)
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Answer by richwmiller(3971)
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Question 259169: solve K= 1/2t(a-b) for a
Answer by nerdybill(2712)
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You can
put this solution on YOUR website!solve K= 1/2t(a-b) for a
.
Start by multiplying both sides by 2:
2K = t(a-b)
Divide both sides by t:
2K/t = a-b
Finally add b to both sides:
2K/t + b = a
Question 257869: A trunk is 4x3x2 ft. What is the longest rod that this trunk can contain?
Answer by richwmiller(3971)
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Question 257718: Construct a box-and-whisker plot for the set of numbers.
348, 234, 146, 384, 247, 487, 276, 221, 303
Answer by richwmiller(3971)
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Question 257710: c=2 (3.14) R
44=2(3.14)R
what is the answer and please show the work
Answer by unlockmath(450)
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You can
put this solution on YOUR website!Hello,
Let's get "R" by itself in this 44=2(3.14)R
So this can be rewritten as:
44=6.28R Now divide both sides by 6.28 to give us:
7.006=Radius of the circle
There we go. This answer can be rounded off to 7
RJ
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