9. klasse

en_9_GM_calculate_area_composite_figure_algebraically.json

DetailsActivityApprovals

{
   "voice_prompt": "",
   "manuscript": {
       "title": {
           "text": "How to Calculate the Area of a Composite Figure Algebraically",
           "audio": "How to calculate the area of a composite figure algebraically"
       },
       "description": {
           "text": "To calculate the area of a composite figure, start by identifying the basic shapes that make up the figure. Once you have identified these shapes, add or subtract their areas as needed.",
           "audio": "To calculate the area of a composite figure, start by identifying the basic shapes that make up the figure. Once you have identified these shapes, add or subtract their areas as needed."
       },
       "scenes": [
           {
               "text": "Suppose you are asked to calculate the area of this composite figure. The figure includes only the variables a and b, representing any positive numbers greater than zero. To find the area, you will use basic algebra.",
               "latex": "",
               "//": "Display a composite figure labeled with variables a and b."
           },
           {
               "text": "There is more than one way to solve this task. You could split the figure into three parts: a square and two rectangles. Then, calculate the area of each and add them together.",
               "latex": "",
               "//": "Show the figure being divided into a square and two rectangles."
           },
           {
               "text": "Another method is to divide the figure into two rectangles and add their areas.",
               "latex": "",
               "//": "Illustrate the figure being divided into two rectangles."
           },
           {
               "text": "Lastly, you could consider starting with a large square and then subtracting the area of the smaller square.",
               "latex": "",
               "//": "Show the large square with the smaller square subtracted."
           },
           {
               "text": "Each method will yield the same result. For now, let's focus on the first method, splitting the figure into three parts.",
               "latex": "",
               "//": "Highlight the three-part division method."
           },
           {
               "text": "To calculate the area using this method, divide the red shape into three distinct parts: a square and two rectangles.",
               "latex": "",
               "//": "Show the figure divided into a square and two rectangles, colored red."
           },
           {
               "text": "Let’s examine the side lengths. The first part is the square located at the top left corner. This square has side lengths of a and a, giving it an area of a times a, which equals a squared.",
               "latex": "a \\times a = a^2",
               "//": "Highlight the square and display the calculation a × a = a²."
           },
           {
               "text": "The second part is the rectangle at the bottom left. This rectangle has side lengths of a and b, so its area is a times b, which is ab.",
               "latex": "a \\times b = ab",
               "//": "Highlight the rectangle and display the calculation a × b = ab."
           },
           {
               "text": "The third part is the rectangle at the top right. This rectangle also has side lengths of a and b, making its area a times b, or ab.",
               "latex": "a \\times b = ab",
               "//": "Highlight the second rectangle and display the calculation a × b = ab."
           },
           {
               "text": "Now that you have the areas of each of these three parts, you can add them together to find the total area. The total area is: a squared plus ab plus ab, which equals a squared plus two ab.",
               "latex": "a^2 + ab + ab = a^2 + 2ab",
               "//": "Show the final calculation with the expression a² + ab + ab = a² + 2ab."
           },
           {
               "text": "Thus, the area of the composite figure is a squared plus 2 ab.",
               "latex": "a^2 + 2ab",
               "//": "Display the final result clearly."
           },
           {
               "text": "To calculate the area of a composite figure, first identify the basic shapes that make up the figure. Then, add or subtract their areas as needed.",
               "latex": "",
               "//": "Recap with visuals of different composite figures."
           },
           {
               "text": "And remember, there is often more than one way to solve a problem.",
               "latex": "",
               "//": "End with a motivational visual or quote."
           }
       ],
       "outro": {
       "text": "To calculate the area of a composite figure, start by identifying the basic shapes that make up the figure. Once you have identified these shapes, add or subtract their areas as needed.",
       "audio": "To calculate the area of a composite figure, start by identifying the basic shapes that make up the figure. Once you have identified these shapes, add or subtract their areas as needed."
   }
}