Question
Jillian plans a pillow pattern before sewing. The parallelogram in the center of the pattern has a base length of 9 inches and a height of 7 inches. She needs to find the area of the fabric surrounding the parallelogram pattern. Which statements below should she apply when solving this problem? Check all that apply.
A parallelogram is inside of a rectangle with height 8 inches and base 16 inches
The parallelogram has a base length of 16 inches and a height of 8 inches.
The area of the parallelogram is (9) (7) = 63.
The total area of the block is 128 square inches.
The area surrounding the parallelograms can be found by adding 63 to 128.
The area surrounding the parallelogram can be found by subtracting 63 from 128.
A parallelogram is inside of a rectangle with height 8 inches and base 16 inches
The parallelogram has a base length of 16 inches and a height of 8 inches.
The area of the parallelogram is (9) (7) = 63.
The total area of the block is 128 square inches.
The area surrounding the parallelograms can be found by adding 63 to 128.
The area surrounding the parallelogram can be found by subtracting 63 from 128.
Answers
GPT-4o mini
To find the area of the fabric surrounding the parallelogram, Jillian needs to apply some statements correctly related to the areas involved. Here's the evaluation of each statement:
1. **A parallelogram is inside of a rectangle with height 8 inches and base 16 inches.**
- This statement is potentially relevant since it indicates that the parallelogram exists within a larger rectangle.
2. **The parallelogram has a base length of 16 inches and a height of 8 inches.**
- This statement is not correct, as it gives different dimensions for the base and height of the parallelogram than those provided (base of 9 inches and height of 7 inches).
3. **The area of the parallelogram is (9) (7) = 63.**
- This statement is correct. The area of the parallelogram can indeed be calculated using the formula for area: Area = base × height = 9 inches × 7 inches = 63 square inches.
4. **The total area of the block is 128 square inches.**
- This statement is relevant if the total area of the rectangle that contains the parallelogram is indeed 128 square inches.
5. **The area surrounding the parallelograms can be found by adding 63 to 128.**
- This statement is incorrect. To find the area surrounding the parallelogram, you do not add the area of the parallelogram to the total area; rather, you need to subtract the area of the parallelogram from the total area.
6. **The area surrounding the parallelogram can be found by subtracting 63 from 128.**
- This statement is correct. The area surrounding the parallelogram can be found by calculating the difference between the total area of the rectangle and the area of the parallelogram: 128 - 63 = 65 square inches.
### Summary:
The statements that Jillian should apply when solving the problem are:
- A parallelogram is inside of a rectangle with height 8 inches and base 16 inches.
- The area of the parallelogram is (9) (7) = 63.
- The total area of the block is 128 square inches.
- The area surrounding the parallelogram can be found by subtracting 63 from 128.
1. **A parallelogram is inside of a rectangle with height 8 inches and base 16 inches.**
- This statement is potentially relevant since it indicates that the parallelogram exists within a larger rectangle.
2. **The parallelogram has a base length of 16 inches and a height of 8 inches.**
- This statement is not correct, as it gives different dimensions for the base and height of the parallelogram than those provided (base of 9 inches and height of 7 inches).
3. **The area of the parallelogram is (9) (7) = 63.**
- This statement is correct. The area of the parallelogram can indeed be calculated using the formula for area: Area = base × height = 9 inches × 7 inches = 63 square inches.
4. **The total area of the block is 128 square inches.**
- This statement is relevant if the total area of the rectangle that contains the parallelogram is indeed 128 square inches.
5. **The area surrounding the parallelograms can be found by adding 63 to 128.**
- This statement is incorrect. To find the area surrounding the parallelogram, you do not add the area of the parallelogram to the total area; rather, you need to subtract the area of the parallelogram from the total area.
6. **The area surrounding the parallelogram can be found by subtracting 63 from 128.**
- This statement is correct. The area surrounding the parallelogram can be found by calculating the difference between the total area of the rectangle and the area of the parallelogram: 128 - 63 = 65 square inches.
### Summary:
The statements that Jillian should apply when solving the problem are:
- A parallelogram is inside of a rectangle with height 8 inches and base 16 inches.
- The area of the parallelogram is (9) (7) = 63.
- The total area of the block is 128 square inches.
- The area surrounding the parallelogram can be found by subtracting 63 from 128.