Final answer:
The height of the parallelogram with a base of 6 inches and an area equal to that of a square with side lengths of 6 inches is 6 inches.
Step-by-step explanation:
- If a square has side lengths of 6 inches, the area of the square can be found using the formula for the area of a square, which is side × side. Therefore, the area is 6 inches × 6 inches = 36 square inches.
- In the case of the parallelogram with a base of 6 inches and an equal area to the square, we use the formula for the area of a parallelogram, which is base × height.
- Since we know the area must be 36 square inches (equal to the area of the square), and the base is 6 inches, we can set up the equation 6 inches × height = 36 square inches to solve for the height.
- Dividing both sides by 6 inches gives us the height: height = 36 square inches / 6 inches = 6 inches. This means the height of the parallelogram is also 6 inches.