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MathNet 2019-part-08 — 179 problems (EN–VI) Question 152

Math Olympiad Vault · MathNet 2019-part-08 — 179 problems (EN–VI)

Question 152

For dinner, Priya is eating grilled pineapple spears. Each spear is in the shape of the quadrilateral $PINE$, with $PI = 6~\mathrm{cm}$, $IN = 15~\mathrm{cm}$, $NE = 6~\mathrm{cm}$, $EP = 25~\mathrm{cm}$, and $\angle NEP + \angle EPI = 60^\circ$. What is the area of each spear, in $\mathrm{cm}^2$?