In a trapezium shaped garden with parallel sides 10 m and 20 m, and height 8 m, find the area of the remaining garden.

Steps to Solve

1. Identify dimensions of the trapezium

The lengths of the parallel sides of the trapezium (garden) are given as $AB = 50 \text{ cm}$ and $CD = 20 \text{ cm}$. The height of the trapezium is $h = 8 \text{ m}$, which we convert to centimeters: $8 \text{ m} = 800 \text{ cm}$.

2. Apply the area formula of a trapezium

The formula for the area ( A ) of a trapezium is given by:

$$ A = \frac{1}{2} \times (b_1 + b_2) \times h $$

where ( b_1 ) and ( b_2 ) are the lengths of the parallel sides.

In our case:

• ( b_1 = 50 \text{ cm} )
• ( b_2 = 20 \text{ cm} )
• ( h = 800 \text{ cm} )

3. Substitute the dimensions into the formula

Now we can substitute these values into the formula:

$$ A = \frac{1}{2} \times (50 + 20) \times 800 $$

4. Calculate the area

First calculate ( (50 + 20) ):

$$ 50 + 20 = 70 $$

Then substitute back in:

$$ A = \frac{1}{2} \times 70 \times 800 $$

Now calculate:

$$ A = \frac{1}{2} \times 56000 = 28000 $$

Thus, the area of the trapezium is:

$$ A = 28000 \text{ cm}^2 $$