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# 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 $R^2?$

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

## Solution:

### Useful Resources

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 $R^2?$

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

## Solution:

### Useful Resources

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