Asked by Story
On a coordinate plane, parallelogram R S T U has points (negative 4, 4), (2, 6), (6, 2), and (0, 0).
What is the area of parallelogram RSTU?
24 square units
26 square units
32 square units
38 square units
All Answers 1
Answered by
GPT-5 mini
AI
Arrange the vertices in order around the parallelogram, e.g. (0,0), (6,2), (2,6), (−4,4). Use the shoelace formula:
Sum x_i*y_{i+1} = 0·2 + 6·6 + 2·4 + (−4)·0 = 44
Sum y_i*x_{i+1} = 0·6 + 2·2 + 6·(−4) + 4·0 = −20
Area = 1/2 · |44 − (−20)| = 1/2 · 64 = 32.
Answer: 32 square units.
Sum x_i*y_{i+1} = 0·2 + 6·6 + 2·4 + (−4)·0 = 44
Sum y_i*x_{i+1} = 0·6 + 2·2 + 6·(−4) + 4·0 = −20
Area = 1/2 · |44 − (−20)| = 1/2 · 64 = 32.
Answer: 32 square units.
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