A) A triangular flag has a height of 15 inches and a base length of 25 inches. Magnolia makes a scale drawing of the flag in which the base length is 10 inches. What is the area of Magnolia's scale drawing?
Solve the problem by computing the actual area from the scale drawing. Show your work. (4 points)
To find the area of the scale drawing, we first need to determine the scale factor by comparing the base lengths of the actual flag and the scale drawing.
Scale factor = Actual base length / Scale base length
Scale factor = 25 inches / 10 inches
Scale factor = 2.5
Since the scale factor is 2.5, we need to square this factor to find the area scale factor, because area is calculated by square units.
Area scale factor = Scale factor^2
Area scale factor = 2.5^2
Area scale factor = 6.25
Now, we can find the area of Magnolia's scale drawing by multiplying the area of the actual flag by the area scale factor.
Actual area = 0.5 * base length * height
Actual area = 0.5 * 25 inches * 15 inches
Actual area = 187.5 square inches
Scale drawing area = Actual area * Area scale factor
Scale drawing area = 187.5 square inches * 6.25
Scale drawing area = 1171.875 square inches
Therefore, the area of Magnolia's scale drawing of the triangular flag is 1171.875 square inches.