Question

Tanya has a garden with a trench around it. The garden is a rectangle with width 2 1/2 m and length 2 m. The trench and garden together make a rectangle with width 3 1/2 m and length 3 m. What is the area of the trench?

Answer 1

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 .

Answer 2

10 1/2 for area, you take length times width so for this you take 3 1/2 x 3 = 10 1/2