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?
The scale drawing on the left is a triangle of 4 as a base, with as its height, the triangle on the right has a height of 9, with an unknown base.
First, calculate the area of the smaller triangle on the left using the formula for the area of a triangle A = 1/2 * base * height:
Area = 1/2 * 4 * 3 = 6 square feet
Next, since the base of the larger triangle is unknown, we can use similar triangles to find the ratio of the heights, which will also be the ratio of the bases.
Let x be the unknown base of the larger triangle.
So, the ratio of heights is 9/3 = x/4
Solving for x:
9/3 = x/4
3 = x/4
12 = x
Therefore, the base of the larger triangle is 12.
Now, calculate the area of the larger triangle:
Area = 1/2 * 12 * 9 = 54 square feet
So, the completed flag will have an area of 54 square feet.