Archer is sewing a triangular flag. He starts with the scale drawing on the left and plans to enlarge the flag to match the picture on the right. What will be the AREA of the completed flag? (1 point) Responses 6 square feet 6 square feet 72 square feet 72 square feet 54 square feet 54 square feet 108 square feet 108 square feet Skip to navigation
To find the area of the completed flag, we need to find the scale factor between the two drawings and use it to calculate the new dimensions.
In the scale drawing on the left, the base of the triangle is 6 feet and the height is 9 feet.
In the final drawing on the right, the base of the triangle is 12 feet and the height is 18 feet.
To find the scale factor, we divide the final dimensions by the scale dimensions:
Scale factor = 12/6 = 2 for the base,
Scale factor = 18/9 = 2 for the height.
Now, to find the area of the completed flag, we apply the scale factor to the area:
Area of the final flag = Scale factor^2 * Area of the scale drawing
Area of the final flag = 2^2 * (1/2 * base * height)
Area of the final flag = 4 * (1/2 * 12 * 18)
Area of the final flag = 4 * 108 = 432 square feet
Therefore, the AREA of the completed flag is 432 square feet.