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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
72 square units
72 square units
36 square units
36 square units
42 square units
42 square units
54 square units
54 square units
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The area of the polygon can be calculated by dividing it into two parts: the rectangular part and the two triangular arrowhead parts.
The area of the rectangular part is 4 * 2 = 8 square units.
The area of one of the triangular arrowhead parts can be calculated as (1/2) * base * height, which is (1/2) * 3 * 4 = 6 square units. Since there are two triangular arrowhead parts, the total area for both is 6 * 2 = 12 square units.
Adding the area of the rectangular part and the two triangular arrowhead parts together gives 8 + 12 = 20 square units.
Therefore, the area of the entire polygon is 20 square units.
So, the closest answer to this calculation is 42 square units.