Shape functions :These functions serve to introduce the concept of polymorphism and object$-$oriented programming. You will be programming two types of objects that represent shapes. The rectangle$\_$t type represents a rectangle shape with a width and length. The triangle$\_$t type represents an equilateral triangle with a length. Both types are based on a base shape$\_$t type that corresponds to the base class in an object$-$oriented language.

$//$ DO NOT INCLUDE ANY OTHER LIBRARIES$/$FILES

$//$ Returns the area of a rectangle

$//$ The shape is guaranteed to be a valid rectangle

double rectangle$\_$area$($void$*$ shape$)$

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rectangle$\_$t$*$ rectangle $=($rectangle$\_$t$*)$shape;

$//$ IMPLEMENT THIS

return $0$;

$\}$

$//$ Returns the area of an equilateral triangle

$//$ The shape is guaranteed to be a valid triangle

$//$ The area of an equilateral triangle is sqrt$(3)/4$ times length squared

double triangle$\_$area$($void$*$ shape$)$

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triangle$\_$t$*$ triangle $=($triangle$\_$t$*)$shape;

$//$ IMPLEMENT THIS

return $0$;

$\}$

$//$ Returns the perimeter of a rectangle

$//$ The shape is guaranteed to be a valid rectangle

double rectangle$\_$perimeter$($void$*$ shape$)$

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rectangle$\_$t$*$ rectangle $=($rectangle$\_$t$*)$shape;

$//$ IMPLEMENT THIS

return $0$;

$\}$

$//$ Returns the perimeter of an equilateral triangle

$//$ The shape is guaranteed to be a valid triangle

double triangle$\_$perimeter$($void$*$ shape$)$

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triangle$\_$t$*$ triangle $=($triangle$\_$t$*)$shape;

$//$ IMPLEMENT THIS

return $0$;

$\}$

$//$ Initializes a rectangle shape

void rectangle$\_$construct$($rectangle$\_$t$*$ shape, const char$*$ name, double width, double length$)$

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$//$ IMPLEMENT THIS

$\}$

$//$ Initializes a triangle shape

void triangle$\_$construct$($triangle$\_$t$*$ shape, const char$*$ name, double length$)$

$\{$

$//$ IMPLEMENT THIS

$\}$

$//$ Compares the area of shape$1$ with shape$2$

$//$ Returns $-1$ if the area of shape$1$ is less than the area of shape$2$

$//$ Returns $1$ if the area of shape$1$ is greater than the area of shape$2$

$//$ Returns $0$ if the area of shape$1$ is equal to the area of shape$2$

int compare$\_$by$\_$area$($shape$\_$t$*$ shape$1,$ shape$\_$t$*$ shape$2)$

$\{$

$//$ IMPLEMENT THIS

return $0$;

$\}$

$//$ Compares the perimeter of shape$1$ with shape$2$

$//$ Returns $-1$ if the perimeter of shape$1$ is less than the perimeter of shape$2$

$//$ Returns $1$ if the perimeter of shape$1$ is greater than the perimeter of shape$2$

$//$ Returns $0$ if the perimeter of shape$1$ is equal to the perimeter of shape$2$

int compare$\_$by$\_$perimeter$($shape$\_$t$*$ shape$1,$ shape$\_$t$*$ shape$2)$

$\{$

$//$ IMPLEMENT THIS

return $0$;

$\}$