AMC 12 Mock Exam 2 Problem 4

Problem 4 of 25

Square $ABCD$ has side length $8$ . Point $E$ lies on side $\overline{BC}$ with $BE=6$ , and point $F$ lies on side $\overline{CD}$ with $CF=2$ . What is the area of triangle $AEF$ ?

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Solution

Remove from the square the three right triangles $ABE$ , $ECF$ , and $FDA$ . Their areas are $\frac12\cdot8\cdot6=24$ , $\frac12\cdot2\cdot2=2$ (since $EC=8-6=2$ and $CF=2$ ), and $\frac12\cdot6\cdot8=24$ (since $DF=8-2=6$ ). The area of $\triangle AEF$ is $64-24-2-24=\boxed{14}$ .

Tagged: area in a square (coordinates)

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