Area of Polygons 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
36 square units
36 square units
54 square units
54 square units
42 square units
42 square units
72 square units
72 square units
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To find the area of the polygon, we need to break it down into smaller shapes and find their individual areas.
1. The rectangular part has a length of 4 and a width of 2, so its area is 4 x 2 = 8 square units.
2. The two triangular parts at the base have a base of 3 and a height of 3. So, the area of each triangle is 1/2 x base x height = 1/2 x 3 x 3 = 4.5 square units. Since there are two triangles, their combined area is 9 square units.
3. The two small triangles on the sides of the rectangle have a base of 1 and a height of 3. So, the area of each triangle is 1/2 x base x height = 1/2 x 1 x 3 = 1.5 square units. Since there are two triangles, their combined area is 3 square units.
Adding the areas of all the smaller shapes together, we get:
8 (rectangle) + 9 (base triangles) + 3 (side triangles) = 20
Therefore, the area of the polygon is 20 square units.
None of the given options match the calculated area of the polygon, so the correct response is not provided.