HDU 1071 The area(求面积）

最新推荐文章于 2024-07-29 14:00:00 发布

原创最新推荐文章于 2024-07-29 14:00:00 发布 · 161 阅读

0 ·

CC 4.0 BY-SA版权

ACM刷题同时被 2 个专栏收录

60 篇文章

订阅专栏

数学

16 篇文章

订阅专栏

本博客介绍了一种计算由抛物线和直线围成区域面积的方法，通过给定三个关键点，利用特定公式计算出所需面积，适用于解决几何问题。

Ignatius bought a land last week, but he didn’t know the area of the land because the land is enclosed by a parabola and a straight line. The picture below shows the area. Now given all the intersectant points shows in the picture, can you tell Ignatius the area of the land?

Note: The point P1 in the picture is the vertex of the parabola.
在这里插入图片描述

Input
The input contains several test cases. The first line of the input is a single integer T which is the number of test cases. T test cases follow.
Each test case contains three intersectant points which shows in the picture, they are given in the order of P1, P2, P3. Each point is described by two floating-point numbers X and Y(0.0<=X,Y<=1000.0).
Output
For each test case, you should output the area of the land, the result should be rounded to 2 decimal places.
Sample Input

2
5.000000 5.000000
0.000000 0.000000
10.000000 0.000000
10.000000 10.000000
1.000000 1.000000
14.000000 8.222222

Sample Output

33.33
40.69

Hint

For float may be not accurate enough, please use double instead of float.

题意描述：
给出三个点p1，p2，p3,然后求出抛物线和直线所围成的面积s
解题方法：
这是一个套用公式的题,公式为: 在这里插入图片描述

#include<stdio.h>
#include<math.h>

int main(void)
{
	int t;
	double x1,y1,x2,y2,x3,y3,s;
	scanf("%d",&t);
	while(t--)
	{
		scanf("%lf%lf",&x1,&y1);
		scanf("%lf%lf",&x2,&y2);
		scanf("%lf%lf",&x3,&y3);
		s=(-(y2-y1)/((x2-x1)*(x2-x1)))*((x3-x2)*(x3-x2)*(x3-x2)/6);
		printf("%.2lf\n",s);
	}
	return 0;
}