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2021 AMC Fall 10B Problem 25

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2021 AMC Fall 10B Problem 25AMC 10 Step by Step

Name: Date: September 13, 2026

Quadrilaterals & Polygon Areas · difficulty 5 of 5 · about 15 min · position P21-25

A rectangle with side lengths $1{ }$ and $3,$ a square with side length $1,$ and a rectangle $R$ are inscribed inside a larger square as shown. The sum of all possible values for the area of $R$ can be written in the form $\tfrac mn$ , where $m$ and $n$ are relatively prime positive integers. What is $m+n?$

A)
$14$
B)
$23$
C)
$46$
D)
$59$
E)
$67$

2021 AMC Fall 10B Problem 25

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