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.

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

GPT-4o mini · Answer

To calculate the area of the composite figure made up of the larger rectangle and the smaller rectangle, we can break it down into two parts:

Area of the larger rectangle
Area of the smaller rectangle

Step 1: Calculate the area of the larger rectangle

We are given the dimensions of the larger rectangle:

Width (length along the right side) = 4 units
Height (length along the left side, end to end) = 5 units

Using the formula for the area of a rectangle: \[ \text{Area} = \text{Width} \times \text{Height} \] \[ \text{Area of larger rectangle} = 4 , \text{units} \times 5 , \text{units} = 20 , \text{square units} \]

Step 2: Calculate the area of the smaller rectangle

We are given the dimensions of the smaller rectangle:

Width (bottom length) = 2 units
Height (same height as the larger rectangle since it's extending down from it) = 3 units

Using the same formula for the area: \[ \text{Area of smaller rectangle} = 2 , \text{units} \times 3 , \text{units} = 6 , \text{square units} \]

Step 3: Calculate the total area of the composite figure

Since the two rectangles are stacked together (with the smaller rectangle extending down from the larger rectangle), we can simply add their areas: \[ \text{Total area} = \text{Area of larger rectangle} + \text{Area of smaller rectangle} \] \[ \text{Total area} = 20 , \text{square units} + 6 , \text{square units} = 26 , \text{square units} \]

Thus, the area of the composite figure is \(\boxed{26}\) square units.