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 in square feet?
triangle on the left is 3in and 4
the triangle on the right is 9in and ?
solve for ?
To find the missing side of the triangle on the right, we can use similar triangles.
Since the two triangles are similar, we can set up a proportion using the corresponding sides:
3/9 = 4/?
Cross multiply to solve for ?:
3 * ? = 4 * 9
3? = 36
? = 12
So, the missing side of the triangle on the right is 12 inches.
Now, to find the area of the completed flag, we need to use the formula for the area of a triangle:
Area = (base * height) / 2
Since the base is 9 inches and the height is 12 inches, we can plug in the values:
Area = (9 * 12) / 2
Area = 108 / 2
Area = 54 square inches
Since 1 square foot is equal to 144 square inches, we can convert the area to square feet:
54 square inches * (1 square foot / 144 square inches) = 0.375 square feet
Therefore, the area of the completed flag will be 0.375 square feet.