Geometry Word Problem

Question

A pedestal for a statue is in the shape of a hexagon formed by a square and two congruent triangles, with the dimensions 7 ft length and 4 feet height. What is the area of the top surface of this pedestal?  a) 19 sq. ft  b) 22 sq ft  c) 25 sq. ft  d) 28 sq, ft

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Answer 1

The diagram.  Draw a square with triangles to left and right attached to it.  The side of the square plus the equal altitudes of the triangle is 7 ft.  The side of the square is the width of the pedestal 4 ft.

The altitude of each triangle is (7-4)/2=3/2, the base is 4. The total area if the pedestal is 4×4=16 for the square part and 4×3/2=6  for the two triangles (each has base 4 altitude 3/2). The total area is 22 ft²