Similarity: Similar Polygons

Think & Click: Similar Polygons in Real World Problems

Now, you try. Complete the Think & Click activity by looking at each problem below, thinking about it, and then clicking on the question to reveal the solution.

You are building a model of the Eiffel Tower. Your model is 12 inches tall and the actual Eiffel Tower is 1063 feet tall. How tall should the antenna be on your model if the actual antenna is 79 feet tall?

12 inches = 1 foot
$the fraction “model” over “actual” equals one-one-thousand-sixty-thirds equals the fraction x over 79; 1 time 79 equals 1063 x; 79 equals 1063 x; 0 point 0 7 4 3 equals x$

0.0743 feet x 12 inches per foot = 0.89 inches

The model antenna should be 0.89 inches.

You didn’t quite aim right when playing pool last time (In the example problem) and you missed the shot. You reset the ball to try again, but this time the ball is just 30 inches from the corner pocket of the 100 inch by 50 inch pool table. How far from the corner should you now hit the ball so that it will bounce and go into the corner pocket?

$thirty-fiftieths equals the fraction x over the quantity 100 minus x; 30 times the quantity 100 minus x equals 50 x; 3000 equals 80x; 37 point 5 equals x$

The ball should hit the rail 37.5 inches from the corner in order to bounce and make it into the opposite corner pocket.

You have to build a model of your bedroom for your Geometry class. Your actual bedroom is 10 feet by 12 feet. The model you are making is 6 inches by 7.2 inches. If the area of a rug in your room is 80 square feet, what will the area of the rug in your model be if it is going to be proportional?

6 inches = 0.5 feet
$the fraction “actual length” over “model length” equals the fraction 10 over 0 point 5; the fraction “actual area” over “model area” equals the fraction 10 squared over 0 point 5 squared equals the fraction 100 over 0 point 25; the fraction 100 over 0 point 25 equals the fraction 80 over x; 100 x equals 0 point 25 times 80; 100 x equals 20; x equals 0 point 2$

0.2 square feet x 12² square inches per square foot equals 28.8 square inches.

Complete the review worksheet for this section before taking the quiz. Download the review worksheet, complete the questions, and then download the answer key to check your work. Make sure to ask your teacher any questions.