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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
54 square units
54 square units
36 square units
36 square units
42 square units
42 square units
72 square units
72 square units
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The area of the polygon can be calculated by dividing it into two triangles and a rectangle.
1. The two triangular edges at the base each have a base of 3 and a height of 3 (perpendicular height of the triangular arrowhead). The area of each triangle is (1/2) * base * height = (1/2) * 3 * 3 = 4.5 square units (each triangle).
2. The rectangle has dimensions of 4 by 2. Therefore, the area of the rectangle is length * width = 4 * 2 = 8 square units.
Therefore, the total area of the polygon is the sum of the areas of the triangles and the rectangle, which is:
2 * 4.5 (for the two triangles) + 8 (for the rectangle) = 9 + 8 = 17 square units.
Therefore, the correct answer is not provided in the options.