Practice problems for area and scale factors.
You may want to read my review if you have not already done so.
You can practice these problems about similar (proportional) figures.
And here are more problems (written in a style similar to probable quiz problems).
1. I drew two pictures of a school. If the larger picture is twice as wide and 3 times as high as the smaller picture, by what factor has the area increased?
2. I have two pictures of a star. The smaller star has an area of 5 cm2. If the larger star is 3 times as wide and 4 times as high as the smaller star, what is its area?
3. I took the same 5 cm2 picture of a star and made it 1 1/2 times as wide and twice as high. What is the area of this new star?
4. I took a picture of a hot dog and stretched it in several different ways. The area of the original hot dog was 3 cm2, and the area of all of the other hot dogs was 12 cm2.
a. The first time, I used a vertical scale factor of 2; what was my horizontal scale factor?
b. The second time, I used a horizontal scale factor of 8, what was the vertical scale factor?
c. The last time, I used a horizontal scale factor of 6, what was the vertical scale factor?
5. I have two pictures of whales. The larger picture was made from the smaller picture, by enlarging by a factor of 2 vertically, and 1.5 horizontally. If the area of the larger whale is 45 cm2, what is the area of the smaller whale?
6. I have two pictures of a tree. the smaller picture was made from the larger picture by compressing by a scale factor of 1/2 vertically, and 2/3 horizonally. If the smaller picture has an area of 6 cm2, what is the area of the larger tree?
7. I have two similar (proportional) pictures of a moon and star. The larger picture was enlarged by 200% on a standard copy machine from the smaller one:
a. If the area of the smaller star is 5 cm2, what is the area of the larger star?
b. If the area of the larger moon is 48 cm2, what is the area of the smaller moon?
8. I have a small picture of the famous painting the Mona Lisa. My picture is 1/5 as wide as the original painting. If my picture is 24 in2, what is the area of the oringinal painting?
9. I have two similar/proportional pictures of a cake. If the smaller cake has area 8 cm2, and the area of the large cake is 72cm2, what is the (length) scale factor that compares the large one to the small one.
10. A newspaper used pictures of houses in a graph showing how house prices have gone up. To show that house prices went up 150%, they showed a house that had been increased by a length scale factor of 1.5.
a. By what factor did the area increase?
b. Do you think this graphic is misleading or not?
11. I have a large plate and a small plate (of the same shape). The diameter of the large plate is 1 1/2 times the diameter of the small plate. The plates are of the same thickness and made of the same material, so that the weight is proportional to the area of the plates. If the small plate weighs 4oz, how much does the large plate weigh?
12. John painted a santa that was 10 inches high, and it used 2 oz of paint. Then he was asked to paint another (similar/proportional) santa that is 30 inches high. How much paint will he use for the larger santa?
13. Jan built a 1/50 scale model of the new library before it was built.
a. If the length along one side of the scale model is 3 feet, what is the length of the corresponding side of the library?
b. If Jan used 2 square feet of glass for the windows in the model, how many square feet of glass will the library have?