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MATH / In convex hexagon ABCDEF, all six sides are congruent, ∠A and ∠D are right angles, and ∠B, ∠C, ∠E, and ∠F are congruent. The area of the hexagonal region is 2116(√(2)+1). Find AB.

Problem

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problem

In convex hexagon ABCDEFABCDEF, all six sides are congruent, ∠A\angle A and ∠D\angle D are right angles, and ∠B\angle B, ∠C\angle C, ∠E\angle E, and ∠F\angle F are congruent. The area of the hexagonal region is 2116(2+1)2116(\sqrt2+1). Find ABAB.
Plain-text mathematical notation (without MathML)
In convex hexagon ABCDEF, all six sides are congruent, ∠A and ∠D are right angles, and  ∠B, ∠C, ∠E, and ∠F are congruent. The area of the hexagonal region is 2116(√(2)+1). Find AB.
Original LaTeX notation
In convex hexagon $ABCDEF$, all six sides are congruent, $\angle A$ and $\angle D$ are right angles, and  $\angle B$, $\angle C$, $\angle E$, and $\angle F$ are congruent. The area of the hexagonal region is $2116(\sqrt2+1)$. Find $AB$.

level

Level 5

type

Geometry

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Source and history

task_id
006a8925-2dc1-5795-82bb-a6bb2a03b77e
task_key
geometry--test--006a8925-2dc1-5795-82bb-a6bb2a03b77e
task_revision_id
1
config / split
geometry / test

Official source

initial import