Question - Calculating Area of an Irregular Figure using Rectangles
Solution:
To find the area of the irregular figure, we can divide the figure into two rectangles, label them A and B as in the image, and then calculate the area for each one before summing them up.The given dimensions for Rectangle A are 6m (height) and 9m (width).The area of Rectangle A = height * width = 6m * 9m = 54m²Rectangle B overlaps with Rectangle A, but from the image, we can deduce that Rectangle B extends beyond Rectangle A by 6 m (since the height of A is 6 m, and they share a common width segment). The total width of Rectangle B is given as 18 m.Therefore, to avoid counting the overlapped area twice, we calculate the area of the extension of Rectangle B.The width of the extension of Rectangle B = total width - width of Rectangle A = 18m - 9m = 9mUsing the height of Rectangle A as the height of Rectangle B (since the heights are the same):The area of the extension of Rectangle B = height * extended width = 6m * 9m = 54m²Finally, we add the areas of Rectangle A and the extension of Rectangle B together to find the total area of the irregular shape:Total area = area of A + area of B's extension = 54m² + 54m² = 108m²So, the area of the irregular figure is 108 square meters.
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