Expert answers to "Find the area of the parallelogram with vertices..." - Plainmath

Michelle Isakson

Answered question

2021-11-16

Find the area of the parallelogram with vertices A(-3,0), B(-1,7), C(9,6), and D(7,-1)

Answer & Explanation

Phisecome

Beginner2021-11-17Added 18 answers

Area of parallelogram with vertices
(-3,0), (-1,7), (9,6) and (7,-1) is given by

A = \frac{1}{2} [x_{1} y_{2} + x_{2} y_{3} + x_{3} y_{4} + x_{4} y_{1} - x_{2} y_{1} - x_{3} y_{1} - x_{3} y_{2} - x_{4} y_{3} - x_{1} y_{4}]

Here,

(x_{1}, y_{1}) = (- 3, 0)

(x_{2}, y_{2}) = (- 1, 7)

(x_{3}, y_{3}) = (9, 6)

(x_{4}, y_{4}) = (7, - 1)

A = \frac{1}{2} ∣ (- 3) (7) + (- 1) 6 + 9 \times (- 1) + 7 \times (0) - 9 \times 7 - 7 \times 6 - (- 3) (- 1)

= \frac{1}{2} | - 21 - 6 - 9 + 0 - 0 - 63 - 42 - 3 |

= \frac{1}{2} (144) = 72

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