Use the image to answer the question.

Question

An illustration shows a rectangle that extends to a smaller rectangle at the bottom left. The length of the bottom rectangle is much lesser on the right. The dimensions are as follows: The larger rectangle shows the right side as 4, truncated bottom length as 3, and left side end to end as 5 including the extended rectangle. The smaller rectangle shows the bottom length as 2. There are 5 right angled symbols to show the perpendicular lines of the two rectangles.

What is the area of the composite figure in square units?(1 point)
square units

Answer 1

To find the area of the composite figure, we first need to calculate the areas of both rectangles separately and then add them together.

1. Area of the larger rectangle:

   • The dimensions are:
     • Length = 4 units
     • Height = 5 units (this includes the smaller rectangle)

   Area of the larger rectangle = length × height \[ \text{Area}_{\text{larger}} = 4 \times 5 = 20 \text{ square units} \]

2. Area of the smaller rectangle:

   • The dimensions are:

     • Length = 2 units
     • Height = the remaining height of the larger rectangle after accounting for the smaller rectangle. Since the larger rectangle's height is 5 and we assume the bottom rectangle takes up a part of this, we find the height of the smaller rectangle:

     Height of the smaller rectangle = Total height of larger rectangle - Bottom height = 5 - 3 = 2 units

   Area of the smaller rectangle = length × height \[ \text{Area}_{\text{smaller}} = 2 \times 2 = 4 \text{ square units} \]

3. Total area of the composite figure: \[ \text{Total Area} = \text{Area}{\text{larger}} + \text{Area}{\text{smaller}} = 20 + 4 = 24 \text{ square units} \]

Thus, the area of the composite figure is 24 square units.