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) Responses 6 square feet 6 square feet 72 square feet 72 square feet 54 square feet 54 square feet 108 square feet 108 square feet
The area of a triangle is given by the formula A = 0.5 * base * height.
In the scale drawing on the left, the base of the triangle is 3 feet and the height is 4 feet. Therefore, the area of the scale drawing is:
A = 0.5 * 3 * 4 = 6 square feet.
To enlarge the scale drawing to match the picture on the right, both the base and height will be enlarged by a scale factor of 6 (since 18/3 = 6 and 24/4 = 6).
The base of the enlarged triangle will be 3 * 6 = 18 feet and the height will be 4 * 6 = 24 feet.
Using the formula for the area of a triangle, we find the area of the enlarged flag to be:
A = 0.5 * 18 * 24 = 216 square feet.
Therefore, the area of the completed flag will be 216 square feet.
wrong
Apologies for the mistake. Let's recalculate the area of the completed flag.
The scale drawing on the left has a base of 3 feet and a height of 4 feet. The area of this scale drawing is:
A = 0.5 * 3 * 4 = 6 square feet.
To enlarge the flag, we need to find the scale factor. The base of the larger flag is 18 feet and the height is 24 feet. Dividing these measurements by the corresponding ones in the scale drawing gives us:
18 / 3 = 6
24 / 4 = 6
So, the scale factor is 6.
Now, we will use this scale factor to find the area of the completed flag:
Base: 3 * 6 = 18 feet
Height: 4 * 6 = 24 feet
A = 0.5 * 18 * 24 = 216 square feet.
Therefore, the correct area of the completed flag will be 216 square feet.