jace ordered a banner in the shape of a parallelogram from a print shop. the print shop charges $1.10 per…

jace ordered a banner in the shape of a parallelogram from a print shop. the print shop charges $1.10 per square foot for banners of any shape and size. what is the approximate cost of the banner before tax? herons formula: area = \\sqrt{s(s - a)(s - b)(s - c)}

jace ordered a banner in the shape of a parallelogram from a print shop. the print shop charges $1.10 per square foot for banners of any shape and size. what is the approximate cost of the banner before tax? herons formula: area = \\sqrt{s(s - a)(s - b)(s - c)}

Answer

Explanation:

Step1: Calculate triangle semi-perimeter

$s = \frac{12 + 9 + 19}{2} = 20$ ft

Step2: Apply Heron's formula for triangle area

$Area_{\triangle} = \sqrt{20(20-12)(20-9)(20-19)} = \sqrt{20 \times 8 \times 11 \times 1} = \sqrt{1760} \approx 41.95$ sq ft

Step3: Find parallelogram area (2×triangle area)

$Area_{\text{parallelogram}} = 2 \times 41.95 = 83.9$ sq ft

Step4: Calculate total cost

$Cost = 83.9 \times 1.10 \approx 92.29$

Answer:

D. $92.30