A triangle flag has a height of 15 inches and a base length of 25 inches. Manholes makes a scale drawing of the flag in which the base length is 10 inches. What is the area of magnolias scale drawing? Solve the problem by computing the actual area from the scale drawing. Show you work
First, let's calculate the area of the actual flag.
Given:
Height of actual flag = 15 inches
Base length of actual flag = 25 inches
Area of triangle = 0.5 * base * height
Area of actual flag = 0.5 * 25 * 15 = 187.5 square inches
Now, to find the area of Magnolia's scale drawing, we need to consider the scale factor used. In this case, the base length of the scale drawing is 10 inches, but the actual base length is 25 inches. The scale factor is 10/25 = 0.4.
To find the area of the scale drawing, we need to square the scale factor and multiply it by the actual area.
Scale factor = 0.4
Area of scale drawing = (scale factor) ^ 2 * Area of actual flag
Area of scale drawing = 0.4^2 * 187.5 = 0.16 * 187.5 = 30 square inches
Therefore, the area of Magnolia's scale drawing is 30 square inches.