Respuesta :
Answer:
Area = 21 unit²
Step-by-step explanation:
We have one point of triangle = (0,0)
The other points can be solved, intersection means
−3x²+20 = x²−16
4x² = 36
x² = 9
x = ±3
when x = 3, y = 3²−16 = 9 -16 = -7 , point is (3,-7)
when x = -3, y = (-3)²−16 = 9 -16 = -7 , point is (-3,-7)
We need to find area of triangle with points (0,0), (3,-7) and (-3,-7).
Area of triangle is given by
[tex]Area =\frac{1}{2}\begin{vmatrix}0 & 0 & 1\\ 3 & -7 & 1\\ -3 & -7 & 1\end{vmatrix}[/tex]
[tex]Area = \frac{1}{2}\left ( 0(-7\times 1-(1\times -7))-0(3\times 1-(1\times -3))+1(3\times -7-(-3\times -7)\right )\\\\Area =\frac{1}{2}(-21-21)=-21=21unit^2[/tex]
Area = 21 unit²
