Which figure has the same area as the parallelogram?
A parallelogram with base 40.2, side length 27.5, and height 21.8.
A parallelogram with base 40.2, side length 27.5, and height 21.8.
A rectangle with width 21.8 and diagonal 27.5.
A 4-sided figure with base 40.2, height 21.8, and side length 27.5.
A rectangle with length 40.2, width 21.8, and diagonal 27.5.
A rectangle with length 40.2, width 21.8, and diagonal 27.5.
To determine which figure has the same area as the given parallelogram, we need to calculate the area of each option and compare it to the area of the parallelogram.
1. Parallelogram with base 40.2, side length 27.5, and height 21.8:
The area of a parallelogram is given by the formula: area = base x height.
So, the area of this parallelogram is: 40.2 x 21.8 = 876.36 square units.
2. Parallelogram with base 40.2, side length 27.5, and height 21.8:
We have already calculated the area of this parallelogram to be 876.36 square units.
3. Rectangle with width 21.8 and diagonal 27.5:
To find the area of a rectangle, we can use the formula: area = length x width.
Since the diagonal forms a right triangle with the sides of the rectangle, we can apply the Pythagorean theorem:
diagonal^2 = length^2 + width^2
27.5^2 = length^2 + 21.8^2
756.25 = length^2 + 475.24
length^2 = 281.01
length = √281.01 ≈ 16.77
The area of the rectangle is then: 16.77 x 21.8 ≈ 365.31 square units.
4. 4-sided figure with base 40.2, height 21.8, and side length 27.5:
This figure is not identified, so we cannot calculate its area.
5. Rectangle with length 40.2, width 21.8, and diagonal 27.5:
Using the same calculations as in option 3:
27.5^2 = 40.2^2 + width^2
756.25 = 1616.04 + width^2
width^2 = 756.25 - 1616.04 ≈ -859.79 (which is not a valid result)
Therefore, this figure is not possible.
From the above calculations, option 3, a rectangle with width 21.8 and diagonal 27.5, has an area of approximately 365.31 square units, which is different from the area of the parallelogram. Thus, none of the given options have the same area as the parallelogram.
To determine whether two shapes have the same area, we need to calculate the area of each shape and compare the results.
For the given options:
1. Parallelogram with base 40.2, side length 27.5, and height 21.8:
Area = base x height = 40.2 x 21.8 = 875.16 square units.
2. Parallelogram with base 40.2, side length 27.5, and height 21.8:
Area = base x height = 40.2 x 21.8 = 875.16 square units.
3. Rectangle with width 21.8 and diagonal 27.5:
Given the width and diagonal, we can use the Pythagorean theorem to find the length of the rectangle:
Length^2 + Width^2 = Diagonal^2
Length^2 + 21.8^2 = 27.5^2
Length^2 + 475.24 = 756.25
Length^2 = 281.01
Length = √281.01 ≈ 16.77
Area = Length x Width = 16.77 x 21.8 ≈ 365.57 square units.
4. 4-sided figure with base 40.2, height 21.8, and side length 27.5:
This option is identical to the first option, as it also describes a parallelogram with the given measurements.
Area = base x height = 40.2 x 21.8 = 875.16 square units.
5. Rectangle with length 40.2, width 21.8, and diagonal 27.5:
Similarly to the third option, we can use the Pythagorean theorem to find the height of the rectangle:
Length^2 + Width^2 = Diagonal^2
40.2^2 + Width^2 = 27.5^2
1616.04 + Width^2 = 756.25
Width^2 = 756.25 - 1616.04
Width^2 = -859.79 (not possible)
Since the result is negative, it is not possible to determine the area of the rectangle using these measurements.
Therefore, the figure that has the same area as the parallelogram with the given measurements is the second option:
- Parallelogram with base 40.2, side length 27.5, and height 21.8.