Question
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 Magnolia's scale drawing, we first need to determine the scale factor used.
The scale factor can be calculated by dividing the actual length by the scaled length:
Scale factor = actual length / scaled length
Scale factor = 25 inches / 10 inches
Scale factor = 2.5
Now, to find the area of Magnolia's scale drawing, we need to square the scale factor and multiply it by the actual area of the flag.
Actual area of the flag:
Area = 0.5 * base length * height
Area = 0.5 * 25 inches * 15 inches
Area = 187.5 square inches
Scaled area of the flag:
Scaled area = (Scale factor)^2 * Actual area
Scaled area = (2.5)^2 * 187.5 square inches
Scaled area = 6.25 * 187.5 square inches
Scaled area = 1171.875 square inches
Therefore, the area of Magnolia's scale drawing is 1171.875 square inches.