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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
36 square units
36 square units
42 square units
42 square units
72 square units
72 square units
54 square units
54 square units
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To find the area of the polygon, we need to find the area of the rectangular part and the two triangular arrowhead parts separately.
The rectangular part has sides measuring 4 and 2, so its area is 4 * 2 = 8 square units.
Each triangular arrowhead part can be divided into three smaller triangles – one with base 1 and height 3, and two with base 2 and height 3. The area of each small triangle is 1/2 * base * height.
For the triangle with base 1 and height 3:
Area = 1/2 * 1 * 3 = 1.5 square units
For each of the triangles with base 2 and height 3:
Area = 1/2 * 2 * 3 = 3 square units
Total area for both triangular arrowhead parts = 2*(1.5 + 3) = 9 square units
Therefore, the total area of the polygon is 8 (rectangle) + 9 (triangular arrowhead parts) = 17 square units.
So, the correct response is not provided in the options given. The area of the polygon is actually 17 square units.