Use the image to answer the question.
the Arkansas flag marked with a length of 18 inches and a width of 12 inches; There is a blue and white rhombus in the middle of the flag with its corners marked 2 inches from the length and width.
What is the area of the rhombus in the middle of the flag? Think creatively about how to find the length of the diagonals.
To find the area of the rhombus in the middle of the flag, we can first calculate the length of the diagonals using the Pythagorean theorem.
Since the rhombus is in the middle of the flag, the length of one side of the rhombus is equal to the width of the flag, which is 12 inches.
Using the Pythagorean theorem on one of the triangles formed by the diagonals, we have:
diagonal^2 = (side/2)^2 + (side/2)^2
diagonal^2 = (12/2)^2 + (12/2)^2
diagonal^2 = 6^2 + 6^2
diagonal^2 = 36 + 36
diagonal^2 = 72
diagonal = √72
diagonal ≈ 8.49 inches
Now that we have the length of the diagonal, we can find the area of the rhombus using the formula:
Area = (diagonal 1 * diagonal 2) / 2
Area = (8.49 * 8.49) / 2
Area = 72 square inches
Therefore, the area of the rhombus in the middle of the Arkansas flag is 72 square inches.
wrong. its 56
I apologize for the mistake in my calculation. Let me rectify it:
To find the area of the rhombus, we need to use the formula:
Area = (d1 * d2) / 2
Where d1 and d2 are the diagonals of the rhombus.
Given that one side of the rhombus is the same as the width of the flag, which is 12 inches, the diagonals can be calculated as follows:
d1 = 12 inches
d2 = 2 * √(12^2 - 2^2) (Using the Pythagorean theorem on one of the triangles)
d2 = 2 * √(144 - 4)
d2 = 2 * √140
d2 ≈ 23.66 inches
Now, we can find the area of the rhombus:
Area = (12 * 23.66) / 2
Area = 283.92 / 2
Area = 141.96 square inches
Therefore, the correct area of the rhombus in the middle of the Arkansas flag is approximately 141.96 square inches, not 56 square inches. Thank you for pointing out the error.
no, the area of the rhombos is 56 inches!
Thank you for the correction.
To calculate the area of the rhombus in the middle of the Arkansas flag:
Given:
Width of flag = 12 inches
Length of flag = 18 inches
Distance from corners to the nearest side = 2 inches
Since the rhombus is in the middle of the flag, the diagonals of the rhombus are the full diagonal of the flag, which can be calculated using the Pythagorean theorem:
Diagonal = √(12^2 + 18^2)
Diagonal = √(144 + 324)
Diagonal = √468
Diagonal ≈ 21.63 inches
Now, we can calculate the area of the rhombus using the formula:
Area = (d1 * d2) / 2
Area = (21.63 * 21.63) / 2
Area = 466.74 / 2
Area = 233.37 square inches
Therefore, the area of the rhombus in the middle of the Arkansas flag is approximately 233.37 square inches. Thank you for your patience and correction.