A triangular flag has a height of 30 inches and a base length of 50 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.
To find the area of Magnolia's scale drawing, we first need to determine the scale factor. The scale factor is found by dividing the actual base length by the scale base length:
Scale factor = Actual base length / Scale base length
Scale factor = 50 inches / 10 inches
Scale factor = 5
Now, to find the height of the scale drawing, we multiply the scale factor by the actual height:
Scale height = Scale factor * Actual height
Scale height = 5 * 30 inches
Scale height = 150 inches
Now we can find the area of the scale drawing by multiplying the scale base length by the scale height and dividing by 2 (since it's a triangle):
Scale area = (Scale base length * Scale height) / 2
Scale area = (10 inches * 150 inches) / 2
Scale area = 1500 square inches
Therefore, the area of Magnolia's scale drawing is 1500 square inches.