anonymous
  • anonymous
HELP - The trapezoids are similar. The area of the smaller trapezoid is 310 m2. Find the area of the larger trapezoid to the nearest whole number. The figure is not drawn to scale. - HELP
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
anonymous
  • anonymous
A. 980 m2 B. 7 m2 C. 1,024 m2 D. 324 m2
mathstudent55
  • mathstudent55
Since you have similar trapezoids, the lengths of the sides are proportional. The areas are proprotional to the square of the scale factor.

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mathstudent55
  • mathstudent55
Here is a simple example that explains my point. |dw:1370836887635:dw|
mathstudent55
  • mathstudent55
Notice the rectangle on the right has both the length and width that are double the ones on the left. The lengths on the right are in a 2:1 ratio to the lengths on the left. So far ok?
anonymous
  • anonymous
Why would it be a 2:1 ?
anonymous
  • anonymous
Like, what makes it a 2:1.
mathstudent55
  • mathstudent55
I'm only talking about my example so far. Don't think of your problem yet. My example is simpler, so follow my example. Then we'll turn to your problem.
anonymous
  • anonymous
Ohh, okay.
mathstudent55
  • mathstudent55
I purposely made the rectangle on the right double the length and double the width of the rectangle on the left. So we have a scale factor for the side lengths of 2:1. The rectangle on the right is 2 times longer and 2 times wider.
mathstudent55
  • mathstudent55
Now this is what you need to understand to be able to solve your problem.
mathstudent55
  • mathstudent55
With the right rectangle having the length and width 2 times larger than the left rectangle, what happened to the area of the right rectangle compared to the area of the left rectangle? How many times larger is the right rectangle's area than the left rectangle's area?
anonymous
  • anonymous
It doubles, doesn't it?
anonymous
  • anonymous
If the rectangle is 2 times larger than the one on the left, the area should be 2 times larger.
mathstudent55
  • mathstudent55
No. Look again. I wrote the areas of the rectangles below them. What are the areas of the rectangles?
anonymous
  • anonymous
Left = 2cm^2 Right = 8cm^2
mathstudent55
  • mathstudent55
Correct. 8 cm^2 is 4 times 2 cm^2
mathstudent55
  • mathstudent55
So you see that when the dimensions of this ploygon are increased by 2 times, the area of the polygon is increased by 4 times. 4 is the same as 2^2. If you increase the dimensions of a polygin by n times, the area of the polygon increases n^2 times.
anonymous
  • anonymous
Ohh, okay! so when the shape is increased by 2, the area increases by 4?
mathstudent55
  • mathstudent55
|dw:1370837844060:dw|
anonymous
  • anonymous
Did you put the two rectangles together in this picture?
mathstudent55
  • mathstudent55
Look at the newest rectangle. The dimensions are now increased by 3 times compared to the original 1 cm by 2 cm rectangle. The new area is 18 cm^2 which is 9 times the original area of 2 cm^2. Why is it 9 times? It's because the increase in area is the square of the increase of the length and width. Since the increase in length and width was 3 times, the increase in area is 3^2 times, or 9 times. Sure enough, 18 cm^2 is 9 times 2 cm^2.
anonymous
  • anonymous
Hmm, Okay.
anonymous
  • anonymous
So is the actual problem I posted up, similar to this one?
anonymous
  • anonymous
@mathstudent55
mathstudent55
  • mathstudent55
Ok. Now lets get back to your problem. Now it becomes a simple problem. 32 m is how many times 18 m? Express it as a fraction.
anonymous
  • anonymous
16/9?
mathstudent55
  • mathstudent55
Excellent. The ratio of the larger length to the smaller length is 32/18 = 16/9.
mathstudent55
  • mathstudent55
What does that mean now as far as the ratio of the larger area to the smaller area?
anonymous
  • anonymous
3:2?
mathstudent55
  • mathstudent55
Not the square root, the square.
mathstudent55
  • mathstudent55
(16/9)^2 = 256/81 The larger area is larger by a factor of 256/81 which is the square of the ratio of the larger length to the smaller length.
anonymous
  • anonymous
OH! Wow... I forgot you had to square it..
mathstudent55
  • mathstudent55
Since the small area is 310 m^2, the large area is 310 * (256/81) m^2
anonymous
  • anonymous
I got 979 61/81
mathstudent55
  • mathstudent55
Now round off to the nearest whole number.
anonymous
  • anonymous
980
anonymous
  • anonymous
980m^2
mathstudent55
  • mathstudent55
That's it
anonymous
  • anonymous
Ha, awesome thank you.
anonymous
  • anonymous
I'm gonna make another question.
mathstudent55
  • mathstudent55
Keep in mind, in a figure, if you double the side, you multiply the area by 2^2=4, and the volume by 2^3 = 8.
mathstudent55
  • mathstudent55
ok

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