A triangle mar flag has a height of 15 inches and a base length of 25 inches. Magician makes a scale drawing of the flag in which the base length is 10 inches. What is the area of magicians drawing? Solve the problem by computing the actual area from the scale drawing.
First, we need to calculate the scale factor used by the magician. The scale factor is found by dividing the actual base length by the drawn base length:
Scale factor = 25 inches / 10 inches = 2.5
Next, we need to calculate the height of the scaled drawing. Since the scale factor is 2.5, the scaled height would be:
Scaled height = 15 inches / 2.5 = 6 inches
Now, we can calculate the area of the scaled drawing by using the scaled base length and height:
Scaled area = (1/2) * base length * height
Scaled area = (1/2) * 10 inches * 6 inches
Scaled area = 30 square inches
Finally, we need to find the actual area of the flag by using the scale factor:
Actual area = Scaled area * (Scale factor)²
Actual area = 30 square inches * (2.5)²
Actual area = 30 square inches * 6.25
Actual area = 187.5 square inches
Therefore, the area of the magician's drawing is 30 square inches and the actual area of the flag is 187.5 square inches.