Table of Contents

- 1 Which square covers more of the plane?
- 2 How do you find the square units of a rectangle?
- 3 What is the difference between units and square units?
- 4 What happens to the area of a square when the length of each side is tripled?
- 5 How many spaces are there in a square?
- 6 How many spaces does a triangle cover in a pattern?

## Which square covers more of the plane?

large square

The large square covers more of the plane, Reasoning varies. Sample reasoning: A large square can fit exactly 9 small squares. A medium square can fit exactly 4 small squares.

## How do you find the square units of a rectangle?

Area is measured in square units such as square inches, square feet or square meters. To find the area of a rectangle, multiply the length by the width. The formula is: A = L * W where A is the area, L is the length, W is the width, and * means multiply.

**How does the area of her new figure compare with that of the original square?**

How does the area of her new figure compare with that of the original square? A: The area of the new figure is greater. We don’t know because neither the side length nor the area of the original square is known.

**What does tile a plane mean?**

In this lesson, we learned about tiling the plane, which means covering a two-dimensional region with copies of the same shape or shapes such that there are no gaps or overlaps.

### What is the difference between units and square units?

A unit square is a square with sides measuring 1 unit, while square units is a unit of measurement.

### What happens to the area of a square when the length of each side is tripled?

If we triple the side, the side of the square each becomes 3x. Therefore, on tripling the side, the area of the square becomes 9 times the original.

**What does not tile the plane mean?**

Summary. In this lesson, we learned about tiling the plane, which means covering a two-dimensional region with copies of the same shape or shapes such that there are no gaps or overlaps.

**What shape Cannot tile a plane?**

A convex polygon with seven or more sides cannot tile the plane.

#### How many spaces are there in a square?

1 small square is 1 space, or 1 unit of area, in the pattern. 2 small squares are 2 spaces. The medium squares cover 2 × 4 = 8 spaces. The large square covers 3 × 3 = 9 spaces. Hence, the large squares cover more of the plane compared to the other squares.

#### How many spaces does a triangle cover in a pattern?

Since the triangles can be matched to the other shapes, let us say 1 triangle is 1 space, or 1 unit of area, in the pattern. So the 7 triangles cover 7 spaces.

**Which type of square covers the most area in the pattern?**

The pattern is repeated, so whichever type of square covers the most area of the first part also covers the most area in the whole pattern. 1 small square is 1 space, or 1 unit of area, in the pattern. 2 small squares are 2 spaces. The medium squares cover 2 × 4 = 8 spaces. The large square covers 3 × 3 = 9 spaces.

**Which shapes can be used to tessellate the plane?**

Every shape of triangle can be used to tessellate the plane. Every shape of quadrilateral can be used to tessellate the plane. In both cases, the angle sum of the shape plays a key role. Since triangles have angle sum 180° and quadrilaterals have angle sum 360°, copies of one tile can fill out the 360° surrounding a vertex of the tessellation.