To find the area of the trapezoid formed by the rectangular section and the right triangles on each side, we first need to calculate the dimensions of the entire shape.
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Calculate the area of the rectangle:
- The rectangle has a length of 10 and a height of 9.
- Area of the rectangle = Length × Height = \( 10 \times 9 = 90 \) square units.
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Calculate the area of each right triangle:
- Each right triangle has a short leg (height) of 9 and a base equal to half the length of the rectangle. The base of each triangle would be the same since they are on opposite sides of the rectangle.
- We need to find that base. Since the trapezoid's longer base is the length of the rectangle, and the triangles' short legs are in line with the rectangle’s height, we have:
- Base (longer leg of the triangle) = \( \sqrt{(9^2) + (5^2)} = \sqrt{81 + 25} = \sqrt{106} \) (but for the area, we'll use the simpler right triangle area formula).
- Each triangle is right-angled with the dimensions being 9 (height) and the height of the rectangle being 10.
- Area of one triangle = \(\frac{1}{2} \times \text{height} \times \text{base} = \frac{1}{2} \times 9 \times 10 = 45\).
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Add the areas of the triangles:
- Since there are two identical triangles, the total area of the triangles = \( 2 \times 45 = 90 \) square units.
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Combine the areas to find the total area of the trapezoid:
- Total Area = Area of Rectangle + Area of Triangles = \( 90 + 90 = 180 \) square units.
Thus, the area of the trapezoid is \( \text{180 units}^2 \).