Math Problem Statement
Solution
The playground consists of three different shapes: a square , a trapezium , and a parallelogram .
To calculate the total area of the playground, we will find the areas of these three shapes individually and then sum them.
1. Square
- Given: Side length of the square is 20 m (from ).
- The area of a square is given by:
2. Trapezium
- The parallel sides of the trapezium are and (from diagram).
- The height of the trapezium is the vertical distance from to , which is 20 m (the same as the side of the square).
- The area of a trapezium is given by: Substituting values:
3. Parallelogram
- The base of the parallelogram is .
- The height of the parallelogram is the vertical distance from to , which is the same as the side of the square, 20 m.
- The area of a parallelogram is given by:
4. Total Area of the Playground
- Now, summing the areas of the three shapes:
Thus, the total area of the playground is 2050 square meters.
Would you like a detailed breakdown of any step?
Here are 5 related questions to consider:
- How would the area change if the side of the square were 25 m instead of 20 m?
- What is the perimeter of the entire playground?
- Can the formula for a trapezium be derived using geometry principles?
- What would happen to the trapezium's area if the height increased to 30 m?
- How does the shape of the parallelogram affect the calculation of the area?
Tip: When dealing with composite shapes, break them down into simpler figures, calculate their areas individually, and then sum them for the total area.
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Math Problem Analysis
Mathematical Concepts
Geometry
Area of composite shapes
Formulas
Area of square = side^2
Area of trapezium = 1/2 × (Base1 + Base2) × Height
Area of parallelogram = Base × Height
Theorems
-
Suitable Grade Level
Grades 7-9
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