HMMT 二月 2020 · 几何 · 第 5 题
HMMT February 2020 — Geometry — Problem 5
题目详情
- Let ABCDEF be a regular hexagon with side length 2. A circle with radius 3 and center at A is drawn. Find the area inside quadrilateral BCDE but outside the circle.
解析
- Let ABCDEF be a regular hexagon with side length 2. A circle with radius 3 and center at A is drawn. Find the area inside quadrilateral BCDE but outside the circle. Proposed by: Carl Joshua Quines √ 3 Answer: 4 3 − π 2 Solution: Rotate the region 6 times about A to form a bigger hexagon with a circular hole. The larger √ √ √ 1 3 hexagon has side length 4 and area 24 3, so the area of the region is (24 3 − 9 π ) = 4 3 − π . 6 2 B C A D F E