In a trapezium shaped garden with parallel sides 10 metre and 20 m and height 8 m a circular flower bed with diameter 8 m was laid. Find the area of the remaining garden.

Understand the Problem

The question is asking for the area of a trapezium-shaped garden after calculating the area of a circular flower bed placed inside it. We need to find the area of the trapezium and subtract the area of the circle from it.

Answer

The area of the trapezium garden minus the area of the circle, calculated using the formulas for both shapes.

Steps to Solve

Find the area of the trapezium To calculate the area of a trapezium, we can use the formula:
$$ A = \frac{1}{2} \times (b_1 + b_2) \times h $$
where ( b_1 ) and ( b_2 ) are the lengths of the two parallel sides (bases), and ( h ) is the height.
Calculate the area of the circular flower bed The area of a circle can be found using the formula:
$$ A = \pi r^2 $$
where ( r ) is the radius of the circle.
Subtract the area of the circle from the area of the trapezium Once we have both areas, we can find the area of the garden by subtracting the area of the flower bed from the area of the trapezium:
$$ \text{Area of garden} = \text{Area of trapezium} - \text{Area of circle} $$

The area of the trapezium-shaped garden minus the circular flower bed is given by:
$$ \text{Area of garden} = A_{\text{trapezium}} - A_{\text{circle}} $$

More Information

This process involves basic geometry and understanding of how to apply formulas for areas of different shapes. It's a common problem in landscaping and design to calculate total usable space after subtracting non-usable areas.

Tips

Not using the correct formula for area, which can lead to incorrect calculations.
Forgetting to convert measurements to the same units, which can result in errors.

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