2007 AMC 8 Problems/Problem 23
Contents
[hide]Problem
What is the area of the shaded pinwheel shown in the grid?
Solution 1
The area of the square around the pinwheel is 25. The area of the pinwheel is equal to Each of the four triangles have a base of 3 units and a height of 2.5 units, and so their combined area is 15 units squared. Then the unshaded space consists of the four triangles with total area of 15, and there are four white corner squares. Therefore the area of the pinwheel is which is
Solution 2
The pinwheel is composed of congruent obtuse triangles whose base measures length and height measures length . Using the area formula for triangles, the pinwheel has an area of
Video Solution
https://www.youtube.com/watch?v=dQw4w9WgXcQ -Happytwin
Video Solution by OmegaLearn
https://youtu.be/abSgjn4Qs34?t=748
~ pi_is_3.14
Video Solution by WhyMath
See Also
2007 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 22 |
Followed by Problem 24 | |
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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