please teach 12 years old student how to solve this question in visual animation and related knowledge. demonstrate the process of the problem solving, step by step.---**Extracted Content:** **Question:** 11. What is the area of the shape drawn in the grid? **Options:** (A) 7 (B) 8 (C) 9 (D) 10 (E) 11 **Chart/Diagram Description:** * **Type:** Geometric figure drawn on a square grid. * **Grid:** A grid of horizontal and vertical lines forming unit squares is shown. The relevant part of the grid is approximately 6 units wide and 4 units tall. * **Shape:** A green shaded polygon with a thick black outline is drawn on the grid. * **Vertices:** The vertices of the polygon appear to be located at the intersections of the grid lines. Assuming the bottom-left visible grid intersection is (0,0) and each square is a unit square, the vertices are at approximately (0,2), (2,4), (3,4), (5,2), (3,0), (2,0). * **Dashed Lines:** There are dashed lines drawn inside the shape. They appear to connect the points where the diagonal edges meet the vertical grid lines at x=2 and x=3, to the points where the diagonal edges meet the horizontal grid line at y=2. Specifically, dashed lines are visible from (0,2) to (2,2), from (2,0) to (2,2), from (2,4) to (2,2), from (5,2) to (3,2), from (3,0) to (3,2), and from (3,4) to (3,2). These dashed lines seem to originate from or terminate at the grid points (2,2) and (3,2). * **Shading:** The interior of the shape is shaded green. * **Area Calculation from Grid:** By counting the number of full unit squares and estimating the area of partial squares based on the grid lines, the area can be determined. There are 4 full unit squares. The boundary lines appear to cut through 8 unit squares diagonally, forming triangles that appear to be half squares. Thus, the area can be estimated as 4 (full squares) + 8 * 0.5 (half squares) = 4 + 4 = 8 unit squares.

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Welcome! Today we'll learn how to find the area of shapes drawn on a grid. A unit square is a 1 by 1 square, and it has an area of 1 square unit. To find the area of any shape, we count how many unit squares fit inside it. Let's look at some simple examples first, then we'll solve our challenging problem step by step! Now let's analyze our green polygon step by step. First, I'll identify all the vertices - the corner points where the edges meet. The vertices are located at coordinates (0,2), (2,4), (3,4), (5,2), (3,0), and (2,0). Next, we can see there are 4 complete unit squares entirely inside the polygon, shown in blue. Around the edges, we have 8 triangular regions shown in yellow, where the polygon's diagonal edges cut through the grid squares. This systematic breakdown will help us calculate the total area accurately. Now let's count the complete unit squares inside our polygon. I'll highlight each complete square one by one. Here's square number 1 - that's 1 square unit. Square number 2 - now we have 2 square units total. Square number 3 - that's 3 square units. And finally square number 4 - giving us 4 complete square units. So far, we have 4 square units from the complete squares. Next, we'll need to calculate the area from the triangular regions around the edges. Now let's understand how to calculate the area of triangular regions. When a diagonal line cuts through a unit square, it creates two right triangles. Each triangle has an area of one-half square unit. Look at this example - the diagonal divides the square into two equal triangles, each with area equals one-half. In our polygon, we identified 8 such triangular regions around the edges. So the total area from triangles is 8 times one-half, which equals 4 square units. Now let's put everything together to find the final answer. We found 4 complete unit squares, which gives us 4 square units. We also found 8 triangular regions, each with area one-half, giving us 8 times one-half equals 4 square units. Adding these together: 4 plus 4 equals 8 square units. Therefore, the area of the green polygon is 8 square units. The correct answer is B, 8. This systematic approach of counting complete squares and calculating triangular areas is a reliable method for finding areas on grid paper.