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FIND THE AREA OF THE COMPLEX FIGURE.
31M
69 M
31 M
12 M
23M
23 M
Since this is a complex figure, to find the area, we need to break it up into smaller, simpler shapes.
First, let's draw a line horizontally from the top-right corner (where the 23m segment meets the 69m segment) to the left. The resulting shapes will be a rectangle on the top and a trapezoid on the bottom.
For the rectangle at the top, we can see that the length is 69m (given) and the width is the difference between the two vertical segments, which is (31m - 12m) = 19m. Now we can find the area of the rectangle by multiplying length and width:
Area of rectangle = Length × Width = 69m × 19m = 1311 m²
Now let's focus on the trapezoid at the bottom. The trapezoid has two parallel sides (bases) which are 31m and 23m (given), and a height of 12m (given). To find the area of a trapezoid, we can use the formula:
Area of trapezoid = (1/2) × (Base1 + Base2) × Height = (1/2) × (31m + 23m) × 12m
Area of trapezoid = (1/2) × (54m) × 12m = 27m × 12m = 324 m²
Finally, we can find the total area of the complex figure by adding the areas of the rectangle and the trapezoid:
Total Area = Area of rectangle + Area of trapezoid = 1311 m² + 324 m² = 1635 m²
So the area of the complex figure is 1635 m².