Answer:
[tex]10\ \text{sq. units}[/tex]
Step-by-step explanation:
The parabola's are
[tex]y=-x^2+9[/tex]
[tex]y=2x^2-3[/tex]
So
[tex]-x^2+9=2x^2-3\\\Rightarrow 12=3x^2\\\Rightarrow \\\Rightarrow x=\sqrt{\dfrac{12}{3}}\\\Rightarrow x=\pm 2[/tex]
[tex]y=-x^2+9=-(2)^2+9\\\Rightarrow y=5[/tex]
[tex]y=-(-2)^2+9=5[/tex]
So, the points at which the parabola's intersect each other is [tex](2,5)[/tex] and [tex](-2,5)[/tex]
The three points of the triangle are [tex](2,5)[/tex], [tex](-2,5)[/tex] and [tex](0,0)[/tex]
Area of a triangle is given by
[tex]A=\dfrac{1}{2}[x_1(y_2-y_3) + x_2(y_3-y_1) + x_3(y_1-y_2)]\\\Rightarrow A=\dfrac{1}{2}[2(5-0)+(-2)(0-5)+0(5-5)]\\\Rightarrow A=10\ \text{sq. units}[/tex]
Area of the triangle formed is [tex]10\ \text{sq. units}[/tex].
