C++ :

#include<iostream>
#include<stdio.h>
using namespace std;

double areaOfintersection(double x1, double y1, double x2, double y2, double x3, double y3, double x4, double y4);

int main()
{
	int N;
	cin >> N;
	double *x1 = new double[N];
	double *x2 = new double[N];
	double *x3 = new double[N];
	double *x4 = new double[N];
	double *y1 = new double[N];
	double *y2 = new double[N];
	double *y3 = new double[N];
	double *y4 = new double[N];
	double *S = new double[N];
	for(int i = 0; i < N; i++)
	{
		cin >> x1[i] >> y1[i] >> x2[i] >> y2[i];
		cin >> x3[i] >> y3[i] >> x4[i] >> y4[i];
		S[i] = areaOfintersection(x1[i], y1[i], x2[i], y2[i], x3[i], y3[i], x4[i], y4[i]);
	}
	for(int i = 0; i < N; i++)
	{
		printf("%0.2lf\n", S[i]);
	}
	delete [] x1;
	delete [] x2;
	delete [] x3;
	delete [] x4;
	delete [] y1;
	delete [] y2;
	delete [] y3;
	delete [] y4;
	delete [] S;
	return 0;
}

//前提：两矩形的边都平行于X轴或者Y轴，x1,x2,x3,x4,y1,y2,y3,y4为矩形对角线的坐标1,2为一个，3,4为一个 
double areaOfintersection(double x1, double y1, double x2, double y2, double x3, double y3, double x4, double y4)
{
	//确保x1 < x2 , y1 < y2 , x3 < x4 , y3 < y4 
	if(x1 > x2)
	{
		x1 += x2;
		x2 = x1 - x2;
		x1 -= x2;
	}
	if(y1 > y2)
	{
		y1 += y2;
		y2 = y1 - y2;
		y1 -= y2;
	} 
	if(x3 > x4)
	{
		x3 += x4;
		x4 = x3 - x4;
		x3 -= x4;
	}
	if(y3 > y4)
	{
		y3 += y4;
		y4 = y3 - y4;
		y3 -= y4;
	} 
	//
	double S = 0;//相交的面积 
	double a = 0;//a，b为相交的矩形的两边长 
	double b = 0;
	bool flag_x42 = x4 >= x2 ? 1 : 0;
	bool flag_x41 = x4 >= x1 ? 1 : 0;
	bool flag_x32 = x3 >= x2 ? 1 : 0;
	bool flag_x31 = x3 >= x1 ? 1 : 0;
	bool flag_y42 = y4 >= y2 ? 1 : 0;
	bool flag_y41 = y4 >= y1 ? 1 : 0;
	bool flag_y32 = y3 >= y2 ? 1 : 0;
	bool flag_y31 = y3 >= y1 ? 1 : 0;   
	//x4 > x2 > x3 > x1, y4 > y2 > y3 > y1 
	if(flag_x42 && flag_x41 && !flag_x32 && flag_x31 && flag_y42 && flag_y41 && !flag_y32 && flag_y31)
	{
		a = x2 - x3;
		b = y2 - y3;
		S = a * b;
	} 
	//x4 > x2 > x3 > x1, y4 > y2 > y1 > y3 
	if(flag_x42 && flag_x41 && !flag_x32 && flag_x31 && flag_y42 && flag_y41 && !flag_y32 && !flag_y31)
	{
		a = x2 - x3;
		b = y2 - y1;
		S = a * b;
	} 
	//x4 > x2 > x1 > x3, y4 > y2 > y3 > y1 
	if(flag_x42 && flag_x41 && !flag_x32 && !flag_x31 && flag_y42 && flag_y41 && !flag_y32 && flag_y31)
	{
		a = x2 - x1;
		b = y2 - y3;
		S = a * b;
	} 
	//x4 > x2 > x1 > x3, y4 > y2 > y1 > y3 
	if(flag_x42 && flag_x41 && !flag_x32 && !flag_x31 && flag_y42 && flag_y41 && !flag_y32 && !flag_y31)
	{
		a = x2 - x1;
		b = y2 - y1;
		S = a * b;
	}
	//x4 > x2 > x3 > x1, y2 > y4 > y3 > y1 
	if(flag_x42 && flag_x41 && !flag_x32 && flag_x31 && !flag_y42 && flag_y41 && !flag_y32 && flag_y31)
	{
		a = x2 - x3;
		b = y4 - y3;
		S = a * b;
	}
	//x4 > x2 > x1 > x3, y2 > y4 > y3 > y1 
	if(flag_x42 && flag_x41 && !flag_x32 && !flag_x31 && !flag_y42 && flag_y41 && !flag_y32 && flag_y31)
	{
		a = x2 - x1;
		b = y4 - y3;
		S = a * b;
	}
	//x4 > x2 > x3 > x1, y2 > y4 > y1 > y3 
	if(flag_x42 && flag_x41 && !flag_x32 && flag_x31 && !flag_y42 && flag_y41 && !flag_y32 && !flag_y31)
	{
		a = x2 - x3;
		b = y4 - y1;
		S = a * b;
	}
	//x4 > x2 > x1 > x3, y2 > y4 > y1 > y3 
	if(flag_x42 && flag_x41 && !flag_x32 && !flag_x31 && !flag_y42 && flag_y41 && !flag_y32 && !flag_y31)
	{
		a = x2 - x1;
		b = y4 - y1;
		S = a * b;
	}
	//x2 > x4 > x3 > x1, y4 > y2 > y3 > y1 
	if(!flag_x42 && flag_x41 && !flag_x32 && flag_x31 && flag_y42 && flag_y41 && !flag_y32 && flag_y31)
	{
		a = x4 - x3;
		b = y2 - y3;
		S = a * b;
	} 
	//x2 > x4 > x1 > x3, y4 > y2 > y3 > y1 
	if(!flag_x42 && flag_x41 && !flag_x32 && !flag_x31 && flag_y42 && flag_y41 && !flag_y32 && flag_y31)
	{
		a = x4 - x1;
		b = y2 - y3;
		S = a * b;
	}
	//x2 > x4 > x3 > x1, y4 > y2 > y1 > y3 
	if(!flag_x42 && flag_x41 && !flag_x32 && flag_x31 && flag_y42 && flag_y41 && !flag_y32 && !flag_y31)
	{
		a = x4 - x3;
		b = y2 - y1;
		S = a * b;
	}
	//x2 > x4 > x1 > x3, y4 > y2 > y1 > y3 
	if(!flag_x42 && flag_x41 && !flag_x32 && !flag_x31 && flag_y42 && flag_y41 && !flag_y32 && !flag_y31)
	{
		a = x4 - x3;
		b = y2 - y3;
		S = a * b;
	}
	//x2 > x4 > x3 > x1, y2 > y4 > y3 > y1 
	if(!flag_x42 && flag_x41 && !flag_x32 && flag_x31 && !flag_y42 && flag_y41 && !flag_y32 && flag_y31)
	{
		a = x4 - x3;
		b = y4 - y3;
		S = a * b;
	}
	//x2 > x4 > x1 > x3, y2 > y4 > y3 > y1 
	if(!flag_x42 && flag_x41 && !flag_x32 && !flag_x31 && !flag_y42 && flag_y41 && !flag_y32 && flag_y31)
	{
		a = x4 - x1;
		b = y4 - y3;
		S = a * b;
	}
	//x2 > x4 > x3 > x1, y2 > y4 > y1 > y3 
	if(!flag_x42 && flag_x41 && !flag_x32 && flag_x31 && !flag_y42 && flag_y41 && !flag_y32 && !flag_y31)
	{
		a = x4 - x3;
		b = y4 - y1;
		S = a * b;
	}
	//x2 > x4 > x1 > x3, y2 > y4 > y1 > y3 
	if(!flag_x42 && flag_x41 && !flag_x32 && !flag_x31 && !flag_y42 && flag_y41 && !flag_y32 && !flag_y31)
	{
		a = x4 - x3;
		b = y4 - y3;
		S = a * b;
	}
	return S;
}