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.
Yes, in mathematical notation, the asterisk (*) is commonly used to represent multiplication.
First, we need to find the scale factor from the actual flag to the scale drawing. The scale factor is found by dividing the actual measurement by the scale measurement. In this case, the actual base length is 25 inches and the scale base length is 10 inches.
Scale factor = Actual measurement / Scale measurement
Scale factor = 25 / 10
Scale factor = 2.5
Next, we need to find the height of the scale drawing by applying the scale factor to the actual height.
Scale height = Actual height / Scale factor
Scale height = 15 / 2.5
Scale height = 6 inches
Now that we have the dimensions of the scale drawing (10 inches for the base length and 6 inches for the height), we can find the area of the scale drawing.
Area of a triangle = (1/2) * base length * height
Area of the scale drawing = (1/2) * 10 * 6
Area of the scale drawing = 30 square inches
Therefore, the area of Magnolia's scale drawing of the flag is 30 square inches.