Answer:
The area of a trench is 5.5 m² .
Step-by-step explanation:
Formula
Area of a rectangle = Length × Breadth
As given
Tanya has a garden with a trench around it.
\(The\ garden\ is\ a\ rectangle\ with\ width\ 2\frac{1}{2}\ m\ and\ length\ 2\ m.\)
i.e
\(The\ garden\ is\ a\ rectangle\ with\ width\ \frac{5}{2}\ m\ and\ length\ 2\ m.\)
Put in the above formula
\(Area\ of\ garden = \frac{5\times 2}{2}\)
= 5 m²
As given
\(The\ trench\ and\ garden\ together\ make\ a\ rectangle\ with\ width\ 3 \frac{1}{2}\ m\ and\ length\ 3 m.\)
i.e
\(The\ trench\ and\ garden\ together\ make\ a\ rectangle\ with\ width\ \frac{7}{2}\ m\ and\ length\ 3 m.\)
\(Area\ of\ garden\ with\ trench = \frac{7\times 3}{2}\)
\(Area\ of\ garden\ with\ trench = \frac{21}{2}\)
= 10.5 m²
Area of the trench = Area of garden with trench - Area of garden
Put the value in the above
Area of the trench = 10.5 m² - 5 m²
= 5.5 m ²
Therefore the area of a trench is 5.5 m² .
