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Scaling Figures: Effects on Areas

Author:Tim Brzezinski
Topic:Area

TASK 1:

Note the manila triangle in the applet below. The pink slider controls the size of the angle with pink vertex. You can move the LARGE POINTS (VERTICES) of this triangle anywhere you'd like AT ANY TIME. Slide the black slider slowly. Pay careful attention to what you see. After doing so, hit the reset button. Then change the size of the angle with pink vertex. Be sure to move the other points around as well. Please answer the question that follows.

Q1:

Note that the "final triangle" has each side TWICE AS LONG as the original manila triangle. How does the AREA of the "final triangle" compare with the AREA of the original manila triangle?

TASK 2:

Note the manila triangle in the applet below. The pink slider controls the size of the angle with pink vertex. You can move the LARGE POINTS (VERTICES) of this triangle anywhere you'd like AT ANY TIME. Slide the black slider slowly. Pay careful attention to what you see. After doing so, hit the reset button. Then change the size of the angle with pink vertex. Be sure to move the other points around as well. Please answer the question that follows.

Q2:

Note that the "final triangle" has each side THREE TIMES AS LONG as the original manila triangle. How does the AREA of the "final triangle" compare with the AREA of the original manila triangle?

Q3:

Suppose the "final triangle" had each side FOUR TIMES AS LONG as the original manila triangle. How would the AREA of the "final triangle" compare with the AREA of the original manila triangle?

Q4:

Suppose the "final triangle" had each side FIVE TIMES AS LONG as the original manila triangle. How would the AREA of the "final triangle" compare with the AREA of the original manila triangle?

Q5:

Suppose the "final triangle" has each side "k" TIMES AS LONG as the original manila triangle. How would the AREA of the "final triangle" compare with the AREA of the original manila triangle? (Express your answer in terms of "k").

Quick (Silent) Demo

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