SOLUTION: start with an equilateral triangle ABC of a side of 2 units and construct three outward-pointing squares ABPQ, BCTU, CARS and the three sides AB, BC and CA. what is the area of the

Question 1066618: start with an equilateral triangle ABC of a side of 2 units and construct three outward-pointing squares ABPQ, BCTU, CARS and the three sides AB, BC and CA. what is the area of the hexagon PQRSTU?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The hexagon is made up of
1 central equilateral triangle of side length 2,
3 squares of side length 2, and
3 isosceles triangles sharing sides of length 2 with the squares.
The surface area of each square is .
The surface area of any triangle ABC can be calculated as
.
For the central, equilateral triangle ABC,
all sides have equal length, and all angles have the same measure:
and .,
so .
The angle between the squares measures
,
because it completes when added to
the right angles of two squares,
plus a angle of the central equilateral triangle.
So each of the three outside isosceles triangles have
two sides of length 2 flanking an angle measuring ,
so the area of each of those 3 isosceles triangles is
.
Since the area of the hexagon is the sum of the areas of
squares, each with ,
and triangles, each with ,
.

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