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MathNet 2018-part-01 — 181 problems (EN–VI) Question 45

Math Olympiad Vault · MathNet 2018-part-01 — 181 problems (EN–VI)

Question 45

The pentagon $ABCDE$, with sides $AB$, $BC$, $CD$, $DE$ and $EA$, satisfies the following conditions:
$$
\bullet \angle ABC = \angle BCD = \angle CDE = 90^\circ
$$
$\bullet$ $CD$ is longer than $AB$.
$\bullet$ $AB = 28$, $BC = 15$, $DE = 10$ and $EA = 13$.
Calculate the area of the pentagon.