Wite a procedure to draw a simple shape (e.g., a triangle) and a function to Exercise calculate its area. Guiding Questions: \( { }^{-} \)What steps are needed to draw the shape? \( { }^{\circ} \) What inputs are needed to calculate the area? - How can you reuse the code?

Below is one example of how you might write a program with two main parts: first, a procedure that “draws” a triangle (using its three vertices) and second, a function that calculates the triangle’s area. In addition, we’ll discuss the inputs and how the code is made reusable. You can adapt the following pseudocode (or Python code) to your programming environment. ────────────────────────────── Step 1. Drawing the Triangle To draw a triangle you need a set of three vertices (points). The typical steps are: 1. Accept the three vertices as inputs. (Each vertex can have an x and y coordinate.) 2. Move the drawing pen (or cursor) to the first vertex. 3. Draw a line from the first vertex to the second. 4. Draw a line from the second vertex to the third. 5. Finally, draw a line from the third vertex back to the first vertex to close the triangle. ────────────────────────────── Step 2. Calculating the Area Common methods to calculate the area of a triangle given its three vertices (x₁, y₁), (x₂, y₂), and (x₃, y₃) uses the determinant (shoelace) formula:   Area = |x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)| / 2 Inputs needed: • The coordinates (x and y values) for each vertex. • (Optional) In other scenarios you might have side lengths, but for our procedure we use vertices. ────────────────────────────── Step 3. Code Reuse To make the code reusable, you can: • Encapsulate the drawing steps in a function (e.g., draw_triangle(vertices)) so you can call it with different sets of points. • Encapsulate the area calculation into its own function (e.g., triangle_area(vertices)). • Parameterize these functions so that if you decide to work with other polygons later, you can write a generic draw_shape(vertices) or area_polygon(vertices) function. ────────────────────────────── Example in Python (using turtle for drawing): Here’s a Python example that demonstrates the concepts: ------------------------------------------------------ import turtle def draw_triangle(vertices): """ Draws a triangle on the screen. Input: vertices - a list of three tuples, e.g. [(x1,y1), (x2,y2), (x3,y3)] """ # Create a turtle object t = turtle.Turtle() # Move to the first vertex without drawing t.penup() t.goto(vertices[0][0], vertices[0][1]) t.pendown() # Draw the three sides of the triangle for vertex in vertices[1:]: t.goto(vertex[0], vertex[1]) # Close the triangle by returning to the starting point t.goto(vertices[0][0], vertices[0][1]) # Optional: Hide the turtle and display drawing until closed t.hideturtle() turtle.done() def triangle_area(vertices): """ Calculates the area of a triangle given its three vertices. Input: vertices - a list of three tuples, e.g. [(x1,y1), (x2,y2), (x3,y3)] Returns: the area of the triangle. """ (x1, y1), (x2, y2), (x3, y3) = vertices area = abs(x1*(y2 - y3) + x2*(y3 - y1) + x3*(y1 - y2)) / 2 return area # Example usage: triangle_vertices = [(0, 0), (100, 0), (50, 80)] print("The area of the triangle is:", triangle_area(triangle_vertices)) draw_triangle(triangle_vertices) ------------------------------------------------------ ────────────────────────────── Explanation: • The draw_triangle function takes a list of three (x,y) coordinate pairs. It then uses turtle graphics to move the drawing cursor:  – The pen is lifted (penup()) to go to the first point.  – The pen is placed down (pendown()), and the turtle draws lines connecting each consecutive vertex.  – Finally, the turtle returns to the first vertex to close the triangle. • The triangle_area function uses the shoelace formula. It accepts the same vertex input and computes the area accordingly. • Both functions are completely independent. That means if you decide to draw another triangle or even a different shape later, you can reuse these functions by simply providing different input. Similarly, if you want to calculate the area of another triangle, you only need to call triangle_area with new vertex data. ────────────────────────────── Summary Answers to the Guiding Questions: 1. What steps are needed to draw the shape?   – Define the three vertices.   – Move to the first vertex.   – Draw lines to the second and third vertices.   – Close the shape by drawing a line back to the first vertex. 2. What inputs are needed to calculate the area?   – The coordinates (x and y) of the three vertices. 3. How can you reuse the code?   – The drawing and area-calculation functionalities are encapsulated in functions. This means you can easily call these functions with different sets of vertices, or extend their logic to support more shapes by adding parameters or writing additional generic functions. This procedure and example code provide a basic but reusable foundation for drawing simple shapes and calculating their areas.