The sailcloth having vertices of 0, 0), (4, 0), and (3, 6), with a sailcloth cost of $11.75 per square yard is $141
The given parameters;
Cost of the sailcloth per square yard = $11.75
Vertices of the sailcloth are; (0, 0), (4, 0), and (3, 6)
The cost of purchasing the sailcloth = The area of the sailcloth × Cost per square yard
Taking the base length as; 4 - 0 = 4
The height = The distance from the x-axis to the highest point on the sailcloth = The highest y-value = 6
Which gives;
The area of the sailcloth = Area of a triangle = [tex]\dfrac{1}{2} \times 4 \times 6 = 12[/tex]
The area of the sailcloth = 12 yard²
The cost of purchasing the sailcloth = 12 yard² × $11.75/yard² = $141
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