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
36 square units
36 square units
54 square units
The area of the polygon can be calculated by finding the area of each individual shape and then adding them together.
The rectangular part has a length of 4 and a width of 2, so its area is 4*2 = 8 square units.
The triangular arrowhead part can be split into two right triangles and a rectangle. The base of each right triangle is 1 and the height is 3, so the area of each right triangle is (1*3)/2 = 1.5 square units. Since there are two right triangles, the total area of the right triangles is 2*1.5 = 3 square units.
The rectangle at the base of the arrowhead part has a length of 4 and a width of 2, so its area is 4*2 = 8 square units.
Adding the areas of the rectangle, the two right triangles, and the rectangular part, we get 8 + 3 + 8 = 19 square units.
Therefore, the area of the polygon is 19 square units.