2022 MMATHS Individual Round Problems/Problem 2

Problem

Triangle $ABC$ has $AB = 3, BC = 4,$ and $CA = 5$ . Points $D, E, F, G, H,$ and $I$ are the reflections of $A$ over $B$ , $B$ over $A$ , $B$ over $C$ , $C$ over $B$ , $C$ over $A$ , and $A$ over $C$ , respectively. Find the area of hexagon $EFIDGH$ .

Solution 1

The area of rectangle $BEHG$ is $6 \cdot 4 = 24$ . The area of triangle $BEF = \frac {8 \cdot 6}{2} = 24$ . The area of rectangle $BDIF$ is $3 \cdot = 24$ . The area of triangle $DBG$ is $\frac {4 \cdot 3}{2} = 6$ . Add them all together to get $\boxed {78}$ .

~Arcticturn

Page

Toolbox

Search

2022 MMATHS Individual Round Problems/Problem 2

Problem

Solution 1