## The Geometry of Gardening

**Work Time**

# Geometry of Gardening

Many gardens have geometrical designs, which often include squares and rectangles, as shown in the image. Gardeners often use grid paper to sketch their designs. Sketch a garden on grid paper. The length of each square on the grid represents 10 meters.

- The coordinates of the corners of the garden are $\left(-10,-5\right)$$\left(20,-5\right)$$\left(-10,15\right)$$\left(20,15\right)$. Plot these points, connecting them in order. What figure is the garden?
- A house with a square base will be built inside the garden area. Three corners of the house have coordinates $\left(0,5\right)$$\left(0,10\right)$$\left(5,5\right)$. What are the coordinates of the fourth corner? What is the area of the house’s base?
- Sand will be used to cover the ground under the house. The layer of sand will be 0.5 meter high. What volume of sand is needed?
- A fence will be built around the house 20 meters away from the house. How long is the fence?
- Outside the fence, grass will be planted. How many square meters is the grassy area?
- Inside the grassy area, a rectangular swimming pool measuring 10 meters by 25 meters will be built. Draw the swimming pool in the grassy area any place you like. What are the coordinates of the corners of this swimming pool?