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..
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To find the area of Magnolia's scale drawing, we can use the scale factor to calculate the new dimensions and then find the area.
Scale factor = Actual base length / Scale drawing base length
Scale factor = 25 inches / 10 inches
Scale factor = 2.5
Height of scale drawing = Actual height x Scale factor
Height of scale drawing = 15 inches x 2.5
Height of scale drawing = 37.5 inches
Area of scale drawing = (1/2) x base length x height
Area of scale drawing = (1/2) x 10 inches x 37.5 inches
Area of scale drawing = 187.5 square inches
Therefore, the area of Magnolia's scale drawing of the flag is 187.5 square inches.
First, we need to find the scale factor by comparing the base lengths of the actual flag and Magnolia's scale drawing.
Scale factor = Actual base length / Scale drawing base length
Scale factor = 25 inches / 10 inches
Scale factor = 2.5
Next, we need to find the height of Magnolia's scale drawing by multiplying the actual height by the scale factor.
Scale drawing height = Actual height x Scale factor
Scale drawing height = 15 inches x 2.5
Scale drawing height = 37.5 inches
Now, we can calculate the area of Magnolia's scale drawing.
Area of scale drawing = (1/2) x base length x height
Area of scale drawing = (1/2) x 10 inches x 37.5 inches
Area of scale drawing = 187.5 square inches
Therefore, the area of Magnolia's scale drawing of the flag is 187.5 square inches.