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Question

Difficulty: MediumPerimeter and Area of 2D Figures

A city park is shaped like a trapezoid with parallel sides measuring 140140 meters and 100100 meters. The perpendicular distance between these parallel sides is 6060 meters. Inside the park, there is a rectangular concrete plaza that measures 4040 meters by 2525 meters. The rest of the park is covered in grass. What is the total area covered in grass, in square meters?

Answer: 6200 m²

Answer

6200
The total area of the trapezoid is found by multiplying the average of the two bases by the height, resulting in 72007200 square meters. The rectangular plaza has an area of 40×25=100040 \times 25 = 1000 square meters. Subtracting the inner plaza's area from the total area yields 62006200 square meters for the grass.

Step-by-Step Solution

1
Calculate the total area of the trapezoidal park.
The area of the park is 72007200 square meters.
The formula for the area of a trapezoid is A=12(b1+b2)hA = \frac{1}{2}(b_1 + b_2)h. Substituting the given dimensions yields A=12(140+100)×60=7200A = \frac{1}{2}(140 + 100) \times 60 = 7200.
2
Calculate the area of the rectangular concrete plaza.
The area of the plaza is 10001000 square meters.
The area of a rectangle is length times width. Calculating 40×2540 \times 25 yields 10001000.
3
Subtract the area of the plaza from the total area of the park to find the grass area.
The total area covered in grass is 62006200 square meters.
The grass covers the portion of the park that is not the plaza. Subtracting 10001000 from 72007200 leaves 62006200.

Key Concept

Calculating and subtracting areas of composite 2D figures
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Topics

Perimeter and Area of 2D Figures

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