Use the image to answer the question.
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
Solve the following problem using what you know about composite figures. What is the area of the figure?
(1 point)
Responses
48 square units
48 square units
30 square units
30 square units
36 square units
36 square units
24 square units
To find the area of the figure, we need to calculate the area of the polygon and subtract the area of the missing rectangular piece.
The area of the polygon is equal to the sum of the areas of its individual sides. The top and bottom sides both have a length of 6 units, so their combined area is 6 * 6 = 36 square units. The right side has a length of 8 units, so its area is 8 * 8 = 64 square units.
Now, we need to find the area of the missing rectangular piece. The left side of the polygon is divided into three parts. The top part has a width of 2 units. Since the top side of the polygon has a length of 6 units, the missing rectangular piece has a height of (6 - 2) = 4 units. We know that the right side of the polygon has a length of 8 units, so the missing rectangular piece has a width of 8 units. Therefore, the area of the missing rectangular piece is 4 * 8 = 32 square units.
To find the area of the figure, we subtract the area of the missing rectangular piece from the total area of the polygon: 36 + 64 - 32 = 68 square units.
Therefore, the area of the figure is 68 square units.