Use the image to answer the question.
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
72 square units
72 square units
42 square units
42 square units
54 square units
54 square units
36 square units
To find the area of the polygon, we first need to calculate the area of the rectangle and the two triangles.
Area of rectangle = length x width = 4 x 2 = 8 square units
Area of one triangle = 0.5 x base x height = 0.5 x 3 x 3 = 4.5 square units (since the base is divided in half by the rectangle, the area of each triangle is half of what it would normally be)
Total area of both triangles = 4.5 + 4.5 = 9 square units
Total area of the polygon = area of rectangle + total area of both triangles = 8 + 9 = 17 square units
Therefore, the correct answer is not listed in the options provided.