A rectangular painting has an area of 720 square inches. It is to be reduced by 1/6 scale factor. What is area of the miniature copy.
720/36=20 sq. in.
Let's say the original painting was 24x30"
24/6=4
30/6=5
4*5=20 sq. in., so the answer checks out!!
Multiply the area of the rectangle by the square of the scale factor to get the area of reduced rectangle.
Reduced area = 720 * (1/6)^2
Reduced area = 720 * (1/36)
Reduced area = 720/6
Reduced area = ? sq in.
To find the area of the miniature copy after reducing it by a scale factor of 1/6, we first need to calculate the scale factor and then use it to determine the new area.
Step 1: Calculate the scale factor.
A scale factor represents the ratio of any two corresponding lengths in two similar figures. In this case, the scale factor of 1/6 means that the dimensions of the miniature copy are 1/6 times smaller than the original painting.
Step 2: Find the dimensions of the original painting.
Since the area of the rectangular painting is given as 720 square inches, we can express it as the product of its length and width: length * width = 720.
Step 3: Calculate the dimensions of the miniature copy.
To find the dimensions of the miniature copy, we need to multiply the original dimensions by the scale factor. So, the length of the miniature copy will be: length * (1/6), and the width of the miniature copy will be: width * (1/6).
Step 4: Calculate the area of the miniature copy.
The area of a rectangle can be found by multiplying its length by its width. Thus, the area of the miniature copy will be: (length * (1/6)) * (width * (1/6)).
Let's solve the problem using these steps:
1. Divide 1 by 6 to find the scale factor: 1/6 = 0.1667 (rounded to four decimal places).
2. Solve the equation length * width = 720 to find the dimensions of the original painting.
3. Multiply the original dimensions by the scale factor to find the dimensions of the miniature copy: length * (1/6) and width * (1/6).
4. Calculate the area of the miniature copy by multiplying the length and width found in step 3: (length * (1/6)) * (width * (1/6)).
Now, you can use these steps to find the area of the miniature copy of the rectangular painting.