A triangular flag has a base length of 21 inches and a height of 49 inches. Dylan makes a scale drawing of the flag in which the length is 6 inches and the height is 14 inches. Dylan needs to find the area of the drawing.

Answer 1

To find the area of the scale drawing, we need to find the scale factor first.

Scale factor = length of drawing / length of actual flag = 6 / 21 = 0.2857
Scale factor = height of drawing / height of actual flag = 14 / 49 = 0.2857

Now, we can find the area of the scale drawing:

Area of scale drawing = (6 inches * 14 inches) = 84 square inches

Since the scale factor is equal for both the length and height, the area of the scale drawing is equal to the actual area of the flag multiplied by the square of the scale factor:

Actual area of flag = (1/2) * base * height = (1/2) * 21 * 49 = 514.5 square inches

Area of scale drawing = Actual area of flag * (scale factor)^2
Area of scale drawing = 514.5 * 0.2857^2
Area of scale drawing = 514.5 * 0.0816
Area of scale drawing ≈ 42 square inches

Therefore, the area of the scale drawing is approximately 42 square inches.