Length is a fundamental concept in mathematics and is used to measure the size of an object in one dimension. It is typically measured in units such as meters, centimeters, feet, or inches. Understanding length is important in various mathematical and scientific contexts.

There are several units used to measure length, including:

- Meter (m)
- Centimeter (cm)
- Kilometer (km)
- Foot (ft)
- Inch (in)

It is often necessary to convert between different units of length. To convert from larger units to smaller units, multiply by the appropriate conversion factor. To convert from smaller units to larger units, divide by the conversion factor.

Length can be measured using various tools, including rulers, meter sticks, tape measures, and measuring tapes. It's important to understand how to read these instruments accurately to obtain precise measurements.

Perimeter is the total distance around the outside of a shape. When finding the perimeter of a shape, you add up all the sides. For example, the perimeter of a rectangle is found by adding the lengths of all four sides.

1. Convert 3.5 meters to centimeters.

*Answer:* 3.5 meters = 350 centimeters

2. If a room is 12 feet long and 10 feet wide, what is the perimeter of the room?

*Answer:* Perimeter = 2(12 ft) + 2(10 ft) = 24 ft + 20 ft = 44 ft

3. A swimming pool is 25 meters long. How many centimeters is this?

*Answer:* 25 meters = 2500 centimeters

4. If a book is 9 inches tall and 6 inches wide, what is the perimeter of the book?

*Answer:* Perimeter = 2(9 in) + 2(6 in) = 18 in + 12 in = 30 in

5. Convert 4.2 kilometers to meters.

*Answer:* 4.2 kilometers = 4200 meters

6. A rope is 15 feet long. What is the length of the rope in yards?

*Answer:* 15 feet = 5 yards

Study GuideSimilarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer keyUsing Similar Polygons Worksheet/Answer keySimilar Polygons Worksheet/Answer keyUsing Similar Polygons Worksheet/Answer keySimilar Polygons

Number and Operations (NCTM)

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

Understand and use ratios and proportions to represent quantitative relationships.

Compute fluently and make reasonable estimates.

Develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios.

Geometry (NCTM)

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects.

Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.

Apply transformations and use symmetry to analyze mathematical situations.

Describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling.

Measurement (NCTM)

Apply appropriate techniques, tools, and formulas to determine measurements.

Solve problems involving scale factors, using ratio and proportion.

Grade 8 Curriculum Focal Points (NCTM)

Geometry and Measurement: Analyzing two- and three-dimensional space and figures by using distance and angle

Students use fundamental facts about distance and angles to describe and analyze figures and situations in two- and three-dimensional space and to solve problems, including those with multiple steps. They prove that particular configurations of lines give rise to similar triangles because of the congruent angles created when a transversal cuts parallel lines. Students apply this reasoning about similar triangles to solve a variety of problems, including those that ask them to find heights and distances. They use facts about the angles that are created when a transversal cuts parallel lines to explain why the sum of the measures of the angles in a triangle is 180 degrees, and they apply this fact about triangles to find unknown measures of angles. Students explain why the Pythagorean Theorem is valid by using a variety of methods - for example, by decomposing a square in two different ways. They apply the Pythagorean Theorem to find distances between points in the Cartesian coordinate plane to measure lengths and analyze polygons and polyhedra.