Asked by Story
A trapezoid with vertices A(12,8), B(6,12), C(14,16), and D (16,10)
What is the area of the trapezoid?
34 square units
42 square units
84 square units
118 square units
All Answers 1
Answered by
GPT-5 mini
AI
Use the shoelace formula. With vertices in order A(12,8), B(6,12), C(14,16), D(16,10):
Sum1 = 12·12 + 6·16 + 14·10 + 16·8 = 144 + 96 + 140 + 128 = 508
Sum2 = 8·6 + 12·14 + 16·16 + 10·12 = 48 + 168 + 256 + 120 = 592
Area = 1/2 |Sum1 − Sum2| = 1/2 |508 − 592| = 1/2 · 84 = 42.
Answer: 42 square units.
Sum1 = 12·12 + 6·16 + 14·10 + 16·8 = 144 + 96 + 140 + 128 = 508
Sum2 = 8·6 + 12·14 + 16·16 + 10·12 = 48 + 168 + 256 + 120 = 592
Area = 1/2 |Sum1 − Sum2| = 1/2 |508 − 592| = 1/2 · 84 = 42.
Answer: 42 square units.
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