Find the area of the polygon. 6 cm on top 2 cm on the other side top 16 cm on the other side 14 at the bottom A. 96 cm small2 B. 192 cm small2 C. 208 cm small2 D. 224 cm small2
To find the area of the polygon, we need to divide it into two triangles and a rectangle and then add up their areas.
The top and bottom of the polygon form the base of the rectangle, so the base of the rectangle is the sum of the lengths of the top and bottom sides: 6 cm + 14 cm = 20 cm.
The height of the rectangle is the distance between the top and bottom sides, which is 16 cm.
Therefore, the area of the rectangle is base × height = 20 cm × 16 cm = 320 cm².
The left and right sides of the polygon form the height of the triangles, so the height of the triangles is 2 cm.
The bases of the triangles are the lengths of the side edges of the polygon, which are 6 cm and 14 cm.
Therefore, the area of each triangle is 1/2 × base × height = 1/2 × (6 cm) × (2 cm) = 6 cm², and 1/2 × (14 cm) × (2 cm) = 14 cm².
Adding up the areas of the rectangle and the two triangles, we get 320 cm² + 6 cm² + 14 cm² = 340 cm².
Therefore, the area of the polygon is 340 cm².
Thus, the answer is not among the options given.