The pair of figures to the right are similar. The area of one figure is given. Find the area of the other figure to the nearest whole number.
Area of smaller parallelogramequals8 ft squared
4 ft
16 ft
The area of the smaller parallelogram is 8 ft². Since the figures are similar, the ratio of their corresponding sides will be the same.
Let the area of the larger parallelogram be x ft². The ratio of the areas is equal to the square of the ratio of their corresponding sides.
Let the sides of the smaller parallelogram be a and b, and the sides of the larger parallelogram be A and B.
So, (A/B)² = (a/b)²
=> A²/B² = a²/b²
=> A/B = a/b
=> A = (a/b) * B
Given that a = 4 ft and A = x ft, we can find B as follows:
4/B = 8/x
4x = 8B
x = 2B
So, the area of the larger parallelogram will be twice the area of the smaller parallelogram:
Area of larger parallelogram = 2 * 8 ft² = 16 ft²
Therefore, the area of the larger parallelogram is 16 ft².
wrong
I apologize for the error. Let's try again.
Since the figures are similar, the ratio of the areas is the square of the ratio of their corresponding sides.
Let the sides of the smaller parallelogram be a and b, and the sides of the larger parallelogram be A and B.
Given that the area of the smaller parallelogram is 8 ft² and one side is 4 ft, we can find the other side by using the formula for the area of a parallelogram, which is base times height.
So, 8 = 4 * b
b = 8 / 4
b = 2 ft
Now, we need to find the corresponding side in the larger parallelogram. Since the figures are similar, the ratio of the sides will be the same.
Let the corresponding side in the larger parallelogram be B.
4 / A = 2 / B
4 / A = 2 / B
B = 2A
Since the area of the larger parallelogram is what we are trying to find, we have:
Area of larger parallelogram = A * B = A * 2A = 2A²
To find the area of the larger parallelogram, you need to find the value of A from the information given. Since the side of the smaller parallelogram is 4 ft, the other side is 2 ft. Therefore, A = 4 ft and:
Area of larger parallelogram = 2 * (4)^2
Area of larger parallelogram = 2 * 16
Area of larger parallelogram = 32 ft²
Therefore, the area of the larger parallelogram is 32 ft².