Show the calculation for the yellow area---**Question Stem:** 由多個長方形組成的圖形，求黃色部分面積 (Figure composed of multiple rectangles, find the area of the yellow part) **Chart Description:** * **Type:** Geometric diagram composed of multiple interconnected rectangles. * **Main Elements:** * The figure is an L-shape formed by arranging several rectangles. * There are four distinct rectangular areas shown within the larger L-shape. * Three of the rectangles have their areas labeled: $50 \text{ cm}^2$, $11 \text{ cm}^2$, and $32 \text{ cm}^2$. * One rectangle is colored yellow and labeled with "? $\text{cm}^2$", indicating its area is unknown. * **Dimensions:** * The overall height on the left side is labeled as $12 \text{ cm}$. * The overall width of the top section is labeled as $6 \text{ cm}$. This $6 \text{ cm}$ corresponds to the width of the rectangle with area $50 \text{ cm}^2$. * The overall width of the bottom section is labeled as $9 \text{ cm}$. * The overall height on the right side is labeled as $8 \text{ cm}$. This $8 \text{ cm}$ corresponds to the height of the rectangle with area $32 \text{ cm}^2$. * **Relative Position:** * The rectangle with area $50 \text{ cm}^2$ is in the top-left position. * The rectangle with area $11 \text{ cm}^2$ is below the $50 \text{ cm}^2$ rectangle, on the bottom-left. * The yellow rectangle with unknown area is to the right of the $50 \text{ cm}^2$ rectangle, in the top-middle position. * The rectangle with area $32 \text{ cm}^2$ is to the right of the yellow rectangle, in the top-right position, and also forms the bottom-right part of the overall L-shape. There is another, unlabeled rectangle below the yellow one and to the left of the $32 \text{ cm}^2$ rectangle, on the bottom-middle. * **Labels and Annotations:** * Dimensions are given in centimeters (cm). * Areas are given in square centimeters ($\text{cm}^2$). * The question mark "?" indicates the value to be found.

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We have an L-shaped figure composed of multiple rectangles. Three rectangles have known areas: fifty square centimeters, eleven square centimeters, and thirty-two square centimeters. We need to find the area of the yellow rectangle marked with a question mark. The figure has overall dimensions of twelve centimeters height on the left, six centimeters width at the top, nine centimeters width at the bottom, and eight centimeters height on the right. Let's solve this step by step. First, we find the height of the top section. Since rectangle one has area fifty square centimeters and width six centimeters, its height is fifty divided by six, which equals twenty-five thirds centimeters. The remaining bottom height is twelve minus twenty-five thirds, which equals eleven thirds centimeters. Rectangle two has area eleven square centimeters and height eleven thirds centimeters, so its width is eleven divided by eleven thirds, which equals three centimeters. Now we can find the yellow rectangle's dimensions. Rectangle three has area thirty-two square centimeters and height eight centimeters, so its width is thirty-two divided by eight, which equals four centimeters. Since the total top width is six centimeters, the yellow rectangle's width is six minus four, which equals two centimeters. Finally, the yellow rectangle's area is width times height: two times twenty-five thirds, which equals fifty thirds or sixteen and two-thirds square centimeters. Let's solve this step by step. First, we find the height of the top section. Since rectangle one has area fifty square centimeters and width six centimeters, its height is fifty divided by six, which equals twenty-five thirds centimeters. The remaining bottom height is twelve minus twenty-five thirds, which equals eleven thirds centimeters. Rectangle two has area eleven square centimeters and height eleven thirds centimeters, so its width is eleven divided by eleven thirds, which equals three centimeters. Now we can find the yellow rectangle's dimensions. Rectangle three has area thirty-two square centimeters and height eight centimeters, so its width is thirty-two divided by eight, which equals four centimeters. Since the total top width is six centimeters, the yellow rectangle's width is six minus four, which equals two centimeters. Finally, the yellow rectangle's area is width times height: two times twenty-five thirds, which equals fifty thirds or sixteen and two-thirds square centimeters. Let me show you an alternative method to verify our answer. We can calculate the total area of the L-shape and subtract the known areas. The top section has area six times twenty-five thirds, which equals fifty square centimeters. The bottom section has area nine times eleven thirds, which equals thirty-three square centimeters. However, this method becomes complex due to overlapping calculations. Our direct method gives us the correct answer: the yellow rectangle has area fifty thirds square centimeters. To summarize our solution: We systematically found the dimensions of each rectangle using the given areas and overall measurements. The key steps were calculating the height of the top section as twenty-five thirds centimeters, finding the width of rectangle two as three centimeters, and determining the yellow rectangle's dimensions as two centimeters by twenty-five thirds centimeters. This gives us the final answer of fifty thirds or sixteen and two-thirds square centimeters for the yellow area.