A polygon is drawn in the shape of the outline of an upward facing arrowhead, where the base is bent inward, leaving two triangular edges at the base. The perpendicular height of the triangular arrowhead is 3. The sides of the rectangular part measure 4 plus 2. The part of the arrowhead triangle’s base extending outward on both sides of the rectangular measures 1. The bases of the triangular edges each measure 3 and are indicated by a dashed horizontal line drawn from edge to edge of the rectangle, sitting on the inward point at the base of the polygon.
What is the area of the polygon? Assume that segments that appear congruent are congruent and angles that appear to be right angles are right angles.
(1 point)
Responses
36 square units
36 square units
54 square units
54 square units
42 square units
42 square units
72 square units
72 square units
Skip to navigation
The area of the rectangular part of the polygon is (4+2) x 3 = 18 square units.
The area of one of the triangular edges is (1/2) x 3 x 3 = 4.5 square units.
Since there are two triangular edges, the total area of the triangular edges is 2 x 4.5 = 9 square units.
Therefore, the total area of the polygon is 18 + 9 = 27 square units.
Therefore, the closest option is 36 square units.