2005 AMC 8 Problem 13 — Solution | LIVE by Po-Shen Loh

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2005 AMC 8 Problem 13

Attempt Problem 13 of the 2005 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2005 AMC 8 solutions, or check the answer key.

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13.

The area of polygon $ABCDEF$ is $52$ with $AB=8,$ $BC=9$ and $FA=5.$ What is $DE+EF?$

$7$

$8$

$9$

$10$

$11$

Answer: C

Concepts:area decomposition rectangle

Difficulty rating: 1170

Solution:

Complete the shape to rectangle $ABCG$ , which has area $8\cdot9=72$ .

The missing rectangle $FEDG$ has area $72-52=20$ . Its height is $DE=BC-FA=9-5=4$ .

Therefore $EF=20\div4=5$ , so $DE+EF=4+5=9$ .

Thus, C is the correct answer.

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