Difference between revisions of "2022 AMC 8 Problems/Problem 18"

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==Solution==
 
==Solution==
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The midpoints of the four sides of every rectangle are the vertices of a rhombus whose area is half the area of the rectangle.
  
 
==See Also==  
 
==See Also==  
 
{{AMC8 box|year=2022|num-b=17|num-a=19}}
 
{{AMC8 box|year=2022|num-b=17|num-a=19}}
 
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{{MAA Notice}}

Revision as of 12:53, 28 January 2022

Problem

The midpoints of the four sides of a rectangle are $(-3,0), (2,0), (5,4),$ and $(0,4).$ What is the area of the rectangle?

$\textbf{(A) } 20 \qquad \textbf{(B) } 25 \qquad \textbf{(C) } 40 \qquad \textbf{(D) } 50 \qquad \textbf{(E) } 80$

Solution

The midpoints of the four sides of every rectangle are the vertices of a rhombus whose area is half the area of the rectangle.

See Also

2022 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 17
Followed by
Problem 19
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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