Difference between revisions of "2013 AMC 8 Problems/Problem 20"
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3. Solve for the area of the circle using the radius pi times radius squared, with will give you 2pi | 3. Solve for the area of the circle using the radius pi times radius squared, with will give you 2pi | ||
4. Divide by 2, getting pi | 4. Divide by 2, getting pi | ||
+ | -Jason Da Goat | ||
==Video Solution== | ==Video Solution== |
Latest revision as of 14:52, 24 August 2025
Problem
A rectangle is inscribed in a semicircle with the longer side on the diameter. What is the area of the semicircle?
Solution
A semicircle has symmetry, so the center is exactly at the midpoint of the 2 side on the rectangle, making the radius, by the Pythagorean Theorem, . The area is
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List of steps
1. Draw a picture, realize the radius comes from the midpoint of rectangle 2. Using the pythagorean theorm, solve for the radius with is square root of 2 3. Solve for the area of the circle using the radius pi times radius squared, with will give you 2pi 4. Divide by 2, getting pi -Jason Da Goat
Video Solution
https://youtu.be/tdh0u9_xjN0 ~savannahsolver
See Also
2013 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 19 |
Followed by Problem 21 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |
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