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### Course: Geometry (FL B.E.S.T.)>Unit 9

Lesson 1: Area problem solving

# Scale factors and area

Sal explore how scale factor affects the area of a scaled figure.

## Want to join the conversation?

• "Polygon Y has an area of 11 square units. Celia drew a scaled version of Polygon Y using a scale factor of 3 and labeled it Polygon Z" is my question. I watched the 2 examples in this video but I am, still not sure how to solve this question. Can somebody please help me?
• The scale factor of 3 means that it is 3 times as long in all dimensions. Since the polygon is a 2d shape, the area of polygon Z will be 9 times as large as the area of polygon Y because 3*3=9 and there are 2 dimensions of the polygon.
• How do you find the actual area from a scale factor area?
• You multiply the area by the scale factor twice.

Here is an example: if we have a rectangle that has a length 3 and a height of 4 and the scale drawing with a scale factor of 2, how many times bigger is the scale drawings area?

The original shape is 3 by 4 so we multiply those to find the area of 12 square units.

The new shape has length of 3x2 (3 x the scale factor) and height of 4x2 (4 x the scale factor). The dimensions of our scale drawing are 6 by 8 which gives us an area of 48 square units. Notice when we found the new dimensions we multiplied the 3 and 4 EACH by the scale factor. So the new area could be found 3 x 4 x scale factor x scale factor.

48/12 = 4 which is the scale factor times the scale factor

with a scale factor of 3
3x4 = 12 units squared
9x12 = 108 units squared
3x4x3x3 = 108 units squared
108/12 = 9 (scale factor x scale factor)
• I am working with a triangle, and he does not include that in this video.
• The same concept applies to any two-dimensional shape.
For example, if you had a triangle with a base measuring 6 units, and a height measuring 3 units, the area would be 9 square units.
If we scale it by 1/3, the triangle's base is 2 units, the height is 1 unit, and the area is 1 square unit.

The dimensions were scaled by 1/3, but the area was scaled by 1/9 (1/3 * 1/3).

Hope this helps!
• I'm 13 seconds in to the video and I dont even wanna keep going it looks so confusing🤯
• What do you need help with? Once you get some practice in it won't be so confusing, trust me :D
• Okay so is the scale factor 9 or 3??
• The scale factor is 3. The 9 is the number that the area increased by, which is the scale factor squared. I hope that helps! Please upvote if it does!
• The first problem was about an arbitrary polygon, not a rectangle. How do you prove that the area changes in proportion to the square of the scaling factor for an arbitrary polygon?
• You may not be able to "prove" it for all figures, but you could for regular polygons which you could find the area of, or you could break down a polygon into simpler figures of triangles and quadrilaterals that you could find the area of, and show that each part would be proportional, then adding all the parts together will show the same proportionality.
• Am i the only on who scrolls through the comments while the video is playing
• Nope because I just did that xD
• Hi, I have a question for everybody to make that I might not understand...in the part of the video:
x1/2 and we turned it in to 4 units to the bottom why is it 4 units? I did not quiet understand. (yes, you can ask me if that did not make sense.To you I´ll always be checking for questions and corrections!)
-Keep up the great work Khan academy you´r doing wonder full!
• how would i get the answer to this problem?

Students are painting the backdrop for the school play. The backdrop is 15 feet wide and 10 feet high. Every 16 inches on the scale drawing represents 5 feet on the backdrop. What is the area of the scale drawing?