To find the perimeter and area of the given trapezoid that consists of a rectangle and a right triangle, we'll first determine the dimensions and then apply the appropriate formulas.
Given Dimensions:
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Rectangle:
- Length (base of trapezoid) = 20 feet
- Width = 15 feet
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Right Triangle:
- Height = 15 feet (this is the same as the width of the rectangle)
- Base = 8 feet
- Hypotenuse = 17 feet
Area Calculation:
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Area of the Rectangle: \[ \text{Area}_{rectangle} = \text{length} \times \text{width} = 20 , \text{ft} \times 15 , \text{ft} = 300 , \text{square feet} \]
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Area of the Triangle: \[ \text{Area}_{triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 8 , \text{ft} \times 15 , \text{ft} = \frac{1}{2} \times 120 , \text{square feet} = 60 , \text{square feet} \]
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Total Area of the Trapezoid: \[ \text{Area}{trapezoid} = \text{Area}{rectangle} + \text{Area}_{triangle} = 300 , \text{square feet} + 60 , \text{square feet} = 360 , \text{square feet} \]
Perimeter Calculation:
The perimeter of the trapezoid consists of the lengths of all the sides:
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Sides of the Polygon:
- Bottom side (rectangle) = 20 feet
- Left side (height of the rectangle) = 15 feet
- Right side (triangle) = hypotenuse = 17 feet
- Base of the triangle = 8 feet
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Calculate the Pairs (Other side of the rectangle is also 15 feet): \[ \text{Perimeter} = \text{bottom} + \text{left} + \text{hypotenuse} + \text{base} = 20 , \text{ft} + 15 , \text{ft} + 17 , \text{ft} + 8 , \text{ft} \]
Adding those: \[ \text{Perimeter} = 20 + 15 + 17 + 8 = 60 , \text{feet} \]
Final Results:
- Area: 360 square feet
- Perimeter: 60 feet
Therefore, the area of the trapezoid is 360 square feet, and the perimeter is 60 feet.
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