Question - Calculating Area of Irregular Figures by Dividing into Rectangles
Solution:
To find the area of an irregular figure, one approach is to divide it into regular shapes, calculate the area of each shape, and then sum the areas.Starting with the first figure:1) This figure can be seen as two rectangles. If we draw a line separating the two rectangles, we have: - Rectangle A with dimensions 18 cm by 6 cm. - Rectangle B with dimensions 12 cm by 6 cm (since 18 cm - 6 cm = 12 cm, the remaining height of the larger rectangle).We’ll find the areas of Rectangle A and Rectangle B separately: - Area of Rectangle A = length × width = 18 cm × 6 cm = 108 cm². - Area of Rectangle B = length × width = 12 cm × 6 cm = 72 cm².Now, add those two areas together to find the total area of the irregular figure: - Total area = Area of Rectangle A + Area of Rectangle B = 108 cm² + 72 cm² = 180 cm².So the area of the first irregular figure is 180 square centimeters.For the second figure:1) This figure can also be seen as two rectangles, let's call them Rectangle C and Rectangle D. - Rectangle C with dimensions 15 m by 6 m. - Rectangle D with dimensions 20 m by 6 m (since 20 m - (15 m - 6 m) = 20 m - 9 m = 11 m the remaining height).The areas of Rectangle C and Rectangle D are calculated as follows: - Area of Rectangle C = length × width = 15 m × 6 m = 90 m². - Area of Rectangle D = length × width = 20 m × 6 m = 120 m².Sum both areas to get the total area of the irregular figure: - Total area = Area of Rectangle C + Area of Rectangle D = 90 m² + 120 m² = 210 m².Thus, the area of the second irregular figure is 210 square meters.
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