2025 AMC 8 Problems/Problem 10: Difference between revisions
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The area of each rectangle is <math>5 \cdot 3 = 15</math>. Then the sum of the areas of the two regions is the sum of the areas of the two rectangles, minus the area of their overlap. To find the area of the overlap, we note that the region of overlap is a square, each of whose sides have length <math>2.5</math> (as they are formed by the midpoint of one of the long sides and a vertex). Then the answer is <math>15+15-2.5^2=\boxed{\textbf{(D)}~23.75}</math>. ~cxsmi | The area of each rectangle is <math>5 \cdot 3 = 15</math>. Then the sum of the areas of the two regions is the sum of the areas of the two rectangles, minus the area of their overlap. To find the area of the overlap, we note that the region of overlap is a square, each of whose sides have length <math>2.5</math> (as they are formed by the midpoint of one of the long sides and a vertex). Then the answer is <math>15+15-2.5^2=\boxed{\textbf{(D)}~23.75}</math>. ~cxsmi | ||
==Solution | |||
==Vide Solution 1 by SpreadTheMathLove== | |||
https://www.youtube.com/watch?v=jTTcscvcQmI | |||
Revision as of 22:15, 29 January 2025
Problem
In the figure below, 
is a rectangle with sides of length 
inches and 
= 3 inches. Rectangle is rotated 
clockwise around the midpoint of side 
to give a second rectangle. What is the total area, in square inches, covered by the two overlapping rectangles?
Solution 1
The area of each rectangle is 
. Then the sum of the areas of the two regions is the sum of the areas of the two rectangles, minus the area of their overlap. To find the area of the overlap, we note that the region of overlap is a square, each of whose sides have length 
(as they are formed by the midpoint of one of the long sides and a vertex). Then the answer is 
. ~cxsmi
