University of Houston math contests

[Albert Chan]

(07-11-2019 03:30 PM)telemachos Wrote:  (–6.94, –1.2), (–5.16, 3.84), (3.4, 2.18), and (2.46, –6.72).

Give the area of this quadrilateral.

Another way is to calculate angles θ between 2 diagonals:

Slope m1 = (2.18 + 1.2) / (3.4 + 6.94) = 3.38 / 10.34
Slope m2 = (-6.72 - 3.84) / (2.46 + 5.16) = -10.56 / 7.62

tan(θ) = (m1-m2) / (1 + m1 m2) ≈ 3.13114
sin(θ) = tan(θ) / √(1 + tan(θ)²) ≈ 0.952598

area = ½ product of diagonals * sin(θ) ≈ ½ √(3.38² + 10.34²) * √(10.56² + 7.62²) * 0.952598 = 67.473