Question

Tanya has a garden with a trench around it. The garden is a rectangle with length 212m2 \dfrac12 \text{m} 2 2 1 ​ m 2, start fraction, 1, divided by, 2, end fraction, start text, m, end text and width 2 m2 \text{ m} 2 m 2, start text, space, m, end text . The trench and garden together make a rectangle with length 312m3 \dfrac12 \text{m} 3 2 1 ​ m 3, start fraction, 1, divided by, 2, end fraction, start text, m, end text and width 3 m3 \text{ m} 3 m 3, start text, space, m, end text . Find the area of just the trench.

Answer 1

Answer:

$9 \dfrac12 m^2$

Step-by-step explanation:

Tanya has a garden with a trench around it.

Tanya's garden is a rectangle with length $\dfrac12 \text{m}$ and width 2m.

The trench and garden together make a rectangle with length $3 \dfrac12 \text{m}$ and width 3m.

We are to determine the area of just the trench.

Area of just the trench = Area of the trench and garden together-Area of the garden

$=(3 \dfrac12 X 3)-(\dfrac12 X 2)\\\\=( \dfrac72 X 3)-1\\\\=\dfrac{21}{2}-1\\\\=9 \dfrac12 m^2$

The area of the trench is $9 \dfrac12 m^2$