The high school debate team is developing a logo to represent their club. A scale drawing of the logo design is presented below, where each unit of the grid represents 3 inches in length.
The team is printing out an enlargement of the new logo, where the enlargement has a height of 105 inches.
The area of the enlargement will be
inches2, which is
times the size of the original scale drawing.
To find the area of the enlargement, we need to calculate the scale factor first by comparing the height of the enlargement to the height of the original scale drawing.
Scale factor = size of enlargement / size of original scale drawing
Scale factor = 105 inches / 3 inches
Scale factor = 35
Now, to find the area of the enlargement:
Area of enlargement = (scale factor)² x area of original scale drawing
Area of enlargement = 35² x (3 inches x 3 inches)
Area of enlargement = 1225 x 9
Area of enlargement = 11,025 inches²
Therefore, the area of the enlargement will be 11,025 inches², which is 1225 times the size of the original scale drawing.