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?
To find the area of the completed flag, we need to first find the scale factor by comparing the lengths of the sides in the scale drawing to the actual dimensions.
In the scale drawing, the base of the triangle is 4 inches and the height is 3 inches. In the actual flag, the base is 8 feet and the height is 6 feet.
To find the scale factor, we divide the actual dimensions by the scale drawing dimensions:
Base scale factor = 8 feet / 4 inches = 96 inches / 4 inches = 24
Height scale factor = 6 feet / 3 inches = 72 inches / 3 inches = 24
Therefore, the scale factor is 24.
Next, we need to find the area of the completed flag. Since the area of a triangle is given by the formula A = 1/2 * base * height, we can find the area of the completed flag by multiplying the dimensions by the scale factor and then calculating the area using the formula.
Base = 8 feet * 24 = 192 inches
Height = 6 feet * 24 = 144 inches
Now we can calculate the area of the completed flag:
A = 1/2 * 192 inches * 144 inches = 13824 square inches
To convert square inches to square feet, we divide by 144 (since 1 square foot = 144 square inches):
13824 square inches / 144 = 96 square feet
Therefore, the area of the completed flag will be 96 square feet.