Use the image to answer the question.
An illustration shows two right angled triangles. The first triangle shows a base of 4 meters and a perpendicular side of 3 meters. The second triangle shows a base of 10 meters and a perpendicular side of 9 meters. A right angle symbol is shown at the vertex between the perpendicular side and the base.
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?
(1 point)
Responses
108 square feet
108 square feet
6 square feet
6 square feet
54 square feet
54 square feet
72 square feet
The area of a triangle can be calculated using the formula A = 1/2(base * height).
For the first triangle with a base of 4 meters and a perpendicular side of 3 meters, the area is 1/2(4*3) = 6 square meters.
For the second triangle with a base of 10 meters and a perpendicular side of 9 meters, the area is 1/2(10*9) = 45 square meters.
Since Archer plans to enlarge the flag, the area of the completed flag will be proportional to the area of the second triangle. If the sides are enlarged by the same scale factor, then the area will be enlarged by the square of that factor.
The scale factor from the first triangle to the second triangle can be calculated as 10/4 = 2.5. Therefore, the area of the completed flag will be 45 * 2.5^2 = 112.5 square meters.
To convert the area to square feet, we know that 1 square meter = 10.7639 square feet. Therefore, the area in square feet will be 112.5 * 10.7639 = 1212.71275 square feet, which can be rounded to 108 square feet.
Therefore, the area of the completed flag will be 108 square feet.