How can you divide the figure into 2 rectangles to find the total area of the figure? Select two choices that represent the areas of the 2 rectangles.
An irregular figure is shown. Starting from the bottom left corner of the figure, the outline of the figure moves up 8 inches, to the right 4 inches, down 4 inches, to the right 4 inches, down 4 inches, and to the left 8 inches to end at the starting point.
A. 2×2=4 square inches
B. 2×4=8 square inches
C. 4×4=16 square inches
D. 4×8=32 square inches
E. 8×8=64 square inches
To divide the figure into 2 rectangles, we can draw a horizontal line cutting the figure in half. The line would be drawn between the two 4-inch segments. This creates a rectangle with dimensions 8 inches by 4 inches on the left and a rectangle with dimensions 8 inches by 2 inches on the right. Therefore, our two choices are:
B. 2×4=8 square inches (for the rectangle on the right)
D. 8×4=32 square inches (for the rectangle on the left)
The total area of the figure would be the sum of the areas of the two rectangles, which is 8+32=40 square inches.
To divide the figure into two rectangles, we need to identify the points where the figure changes direction. Let's go through the movements step by step:
1. "Moves up 8 inches": This creates a vertical side of length 8 inches.
2. "Moves to the right 4 inches": This creates a horizontal side of length 4 inches.
3. "Moves down 4 inches": This creates a vertical side of length 4 inches.
4. "Moves to the right 4 inches": This creates a horizontal side of length 4 inches.
5. "Moves down 4 inches": This creates a vertical side of length 4 inches.
6. "Moves to the left 8 inches to end at the starting point": This creates a horizontal side of length 8 inches.
Based on these movements, the figure can be divided into two rectangles as follows:
- The first rectangle has dimensions 8 inches (height) by 4 inches (width).
- The second rectangle has dimensions 4 inches (height) by 8 inches (width).
Now, let's find the areas of the two rectangles:
Area of the first rectangle = 8 inches (height) × 4 inches (width) = 32 square inches.
Area of the second rectangle = 4 inches (height) × 8 inches (width) = 32 square inches.
So, the correct choices representing the areas of the two rectangles are:
D. 4×8=32 square inches
D. 4×8=32 square inches
To divide the figure into 2 rectangles and find the total area, you need to identify the dimensions of each rectangle.
Based on the given information, let's analyze the movements of the figure:
1. Starting from the bottom left corner, moving up 8 inches results in the vertical side of the first rectangle.
2. Moving to the right 4 inches creates the horizontal side of the first rectangle.
3. Moving down 4 inches forms the vertical side of the second rectangle.
4. Moving to the right 4 inches completes the horizontal side of the second rectangle.
5. Finally, moving down 4 inches and to the left 8 inches forms the remaining sides of the figure.
Now, let's determine the dimensions of the rectangles:
- Rectangle 1: The vertical side is 8 inches, and the horizontal side is 4 inches. Therefore, the area of rectangle 1 is 8 × 4 = 32 square inches.
- Rectangle 2: The vertical side is 4 inches, and the horizontal side is 4 inches. Thus, the area of rectangle 2 is 4 × 4 = 16 square inches.
Therefore, the correct choices for the areas of the two rectangles are:
D. 4×8=32 square inches (for rectangle 1)
C. 4×4=16 square inches (for rectangle 2)