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June 29, 2021

AMC 8 2018 Problem 24 | American Mathematics Competitions

This is a solution to a problem from American Mathematics Competition (AMC) 8 2020 Problem 18 based on Geometry.

AMC 8 2018 Problem 24

In the cube $ABCDEFGH$ with opposite vertices $C$ and $E,$ $J$ and $I$ are the midpoints of edges $\overline{FB}$ and $\overline{HD},$ respectively. Let $R$ be the ratio of the area of the cross-section $EJCI$ to the area of one of the faces of the cube. What is $R^2?$

AMC 8 2018 Problem 24

(A) $\frac{5}{4}$ (B) $ \frac{4}{3} $ (C) $ \frac{3}{2} $ (D) $ \frac{25}{16}$  (E)  $\frac{9}{4}$.

Solution:

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