179k views
3 votes
My rabbit Nibbles lives in a moveable pen and helps to keep the grass short. The pen is rectangular and measures 3m by 2m, as shown in the diagram, where the arrow indicates North. On successive days, the pen is moved 1m East, 2m South, 1m West and 2m North.

What is the total area, in square metres, of the region of grass which Nibbles can nibble?

User Ian Samz
by
8.0k points

1 Answer

6 votes

Answer:

We can break down the total area of grass that Nibbles can nibble into two parts: the original rectangular pen, and the additional grass that Nibbles can reach as the pen is moved.

The area of the original rectangular pen is:

A1 = length x width = 3m x 2m = 6 square meters

To calculate the area of the additional grass, we can visualize the movements of the pen. The pen moves 1 meter to the east, 2 meters to the south, 1 meter to the west, and 2 meters to the north. This creates an irregular pentagon shape, as shown in the diagram below:

```

+-------+

| |

| |

E |

+----+---+ |

| S|

| |

| |

| |

| |

| |

+-----------+

W

```

To calculate the area of this irregular pentagon, we can divide it into two triangles and one rectangle:

- The east and west sides of the pen form a rectangle with dimensions 1m x 2m, for an area of 2 square meters.

- The south side of the pen creates a right triangle with legs of 2m and 1m, for an area of (1/2) x base x height = 1 square meter.

- The north side of the pen creates a right triangle with legs of 2m and 1m, for an area of (1/2) x base x height = 1 square meter.

Therefore, the total area of grass that Nibbles can nibble is:

A = A1 + 2 + 1 + 1 = 10 square meters.

So the answer is 10 square meters.

User Mariusz Nowak
by
7.7k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories