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?
Find the area with the first triangle of 4 ft, 3 ft and the second triangular 9 ft. and ?, which is the area you have to find
To find the area of the enlarged flag, we first need to find the scale factor by comparing the corresponding sides of the two triangles.
The scale factor is given by:
Scale factor = (corresponding side of second triangle) / (corresponding side of first triangle)
Scale factor = 9 ft / 3 ft = 3
Next, we need to use the scale factor to find the missing side of the enlarged flag.
Missing side of the enlarged flag = Scale factor * corresponding side of first triangle
Missing side of the enlarged flag = 3 * 4 ft = 12 ft
Now that we have all the sides of the enlarged flag, we can calculate the area using Heron's formula:
s = (4 + 3 + 12) / 2 = 9.5
Area = sqrt(s*(s-4)*(s-3)*(s-12)) = sqrt(9.5*5.5*6.5*3.5) = sqrt(1128.875) ≈ 33.6 sq ft
Therefore, the area of the completed flag will be approximately 33.6 square feet.