/* Triangle Properties (15 points)

 Problem Statement:
		 
 Given parameters b and h which stand for the base and the height 
 of an isosceles triangle (i.e., a triangle that has two equal sides), 
 write a C program that calculates: 
 
   * the area of the triangle
   * the perimeter of the triangle
   * the volume of the cone formed by spinning the triangle around the line h

 The program must prompt the user to enter b and h.
 The program must define and use the following three functions:
		
     getArea(base, height)       //calculates and returns the area of the triangle
     getPerimeter(base, height)  //calculates and returns the perimeter
     getVolume(base, height)     //calculates and returns the volume

 Format the results so that only three digits after the decimal point are displayed.

 
  Math refresher: Isosceles triangle    

       ^
      /|\           area = (b*h)/2
   a / | \ a        perimeter = b + 2*a
    /  |h \         volume = (1/3)*(area of cone's base)*(height)  
   /   |   \               
   ---------
     b                               
 
 
  Checking with base=6, height=4:
     Area = 12.000
     Petimeter = 16.000
     Volume = 37.699
 */
 
 
 
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
 

float getArea(float b, float h)
{
	return (b*h)/2.0;
}

float getPerimeter(float b, float h)
{
	float a; // first find a which is unknown
	a = sqrt( (b/2)*(b/2) + h*h );
	return b + 2*a;
}
 
float getVolume(float b, float h)
{
	float area=M_PI*pow(b/2,2);
	return (1.0/3.0)*area*h;
} 
 

int main()
{
     float height, base;
     float area, perimeter, volume;
     
     printf("Input the base of the Isosceles triangle: ");
     scanf("%f", &base);
     
     printf("Input the height of the Isosceles triangle: ");
     scanf("%f", &height);
     
     area = getArea(base, height);
     perimeter = getPerimeter(base, height);
     volume = getVolume(base, height);
     
     printf("\n\n"); 
     printf("Area = %7.3f\n", area);
     printf("Perimeter = %7.3f\n", perimeter);
     printf("Volume = %7.3f\n\n", volume);
     
     system("pause");
}