An illustration shows a polygon where the top, right, and bottom sides are perpendicular to each other. A smaller rectangular piece is missing from the center of the left side of the polygon inward. The dimensions are as follows: the top side is 6, the right side is 8, and the bottom side is 6. The left side is divided into three parts. It shows a vertical width of 2 from the top

Question

Solve the following problem using what you know about composite figures. What is the area of the figure?

(1 point)
Responses

36 square units
36 square units

24 square units
24 square units

48 square units
48 square units

30 square units
30 square units

Answer 1

To find the area of the given polygon, we can break it down into simpler shapes.

The polygon appears to resemble a rectangle with a missing rectangular piece.

1. Calculate the area of the large rectangle:

   • The dimensions of the large rectangle can be derived from the given sides.
   • Width (top and bottom sides) = 6
   • Height (right side) = 8
   • Area of the large rectangle = Width × Height = 6 × 8 = 48 square units

2. Calculate the area of the missing rectangular piece:

   • According to the problem, the left side is divided into three parts, with the top vertical width being 2.
   • The height of the missing rectangular piece is the remaining part of the left side from the top to the bottom. Since the total height of the figure is 8 units and 2 units are accounted for at the top, the remaining height = 8 - 2 = 6 units.
   • The width of the missing rectangular piece is not provided but since it’s on the left side and divided vertically, let’s assume it spans the entire height of the rectangle alongside the length of the width, which is effectively the same as the top/bottom width of the polygon.
   • Thus, the area of the missing rectangular piece = Width × Height = Width × (remaining height) = 2 units (width) × 6 units (height) = 12 square units

3. Calculate the area of the remaining figure:

   • Area of the remaining figure = Area of the large rectangle - Area of the missing rectangular piece
   • Remaining area = 48 square units - 12 square units = 36 square units

Thus, the area of the figure is 36 square units.

So the correct response is: 36 square units.