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)
The left triangle features a right triangle with 3 on the and 4 on the bottom and the right triangle also features a right triangle with 9 on the right but the number on the bottom is unknown
To find the area of the completed flag, we need to calculate the area of the original triangle and then scale it up to match the larger triangle.
The area of a triangle can be calculated using the formula: Area = 0.5 * base * height
For the original triangle:
Base = 4
Height = 3
Area = 0.5 * 4 * 3 = 6 square units
To find the area of the larger triangle, we can set up a proportion based on the scale factor. The scale factor is the ratio of the corresponding sides of the two triangles. In this case, the scale factor is 9 (corresponding to the height of the triangles).
So, to find the height of the larger triangle:
9 = x / 3
x = 27
Now that we have the height of the larger triangle, we can calculate the base of the larger triangle using the original base and height ratio:
9 = y / 4
y = 36
Now, to find the area of the larger triangle:
Base = 36
Height = 27
Area = 0.5 * 36 * 27 = 486 square units
Therefore, the AREA of the completed flag will be 486 square units.