How to draw a triangle equal in area with a hexagon
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It is straightforward to construct (straight-edge and compass) an isosceles triangle with area equal to a given triangle △ABC△ABC, for instance as follows:
Construct the line through AA parallel to BCBC(demonstration of method);Construct the perpendicular bisector of BCBC(demonstration of method);The perpendicular from (2) meets the line from (1) at DD; draw △DBC△DBC.
This triangle is isosceles, since DD is equidistant from BB and CC, and has the same base and altitude as △ABC△ABC so has the same area.
Construct the line through AA parallel to BCBC(demonstration of method);Construct the perpendicular bisector of BCBC(demonstration of method);The perpendicular from (2) meets the line from (1) at DD; draw △DBC△DBC.
This triangle is isosceles, since DD is equidistant from BB and CC, and has the same base and altitude as △ABC△ABC so has the same area.
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