A square is a quadrilateral with four equal sides and four right angles. The properties of a square include:

- All four sides are of equal length
- All four angles are right angles (90 degrees)
- The diagonals are of equal length and bisect each other at right angles
- The diagonals divide the square into four congruent right-angled triangles
- The perimeter of a square is given by P = 4s, where s is the length of a side
- The area of a square is given by A = s
^{2}, where s is the length of a side

To find the area and perimeter of a square, you can use the following formulas:

Perimeter (P) = 4 x side length (s)

Area (A) = side length (s) x side length (s)

Here's a sample problem to practice:

**Problem:** Find the perimeter and area of a square with a side length of 5 units.

**Solution:** To find the perimeter:
P = 4 x 5 = 20 unitsTo find the area:
A = 5 x 5 = 25 square units

Remember, the key to solving problems involving squares is to understand the properties and use the appropriate formulas to find the perimeter and area.

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Measurement (NCTM)

Understand measurable attributes of objects and the units, systems, and processes of measurement.

Understand such attributes as length, area, weight, volume, and size of angle and select the appropriate type of unit for measuring each attribute.

Understand the need for measuring with standard units and become familiar with standard units in the customary and metric systems.

Understand that measurements are approximations and how differences in units affect precision.

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

Select and apply appropriate standard units and tools to measure length, area, volume, weight, time, temperature, and the size of angles.

Grade 5 Curriculum Focal Points (NCTM)

Geometry and Measurement and Algebra: Describing three-dimensional shapes and analyzing their properties, including volume and surface area

Students relate two-dimensional shapes to three-dimensional shapes and analyze properties of polyhedral solids, describing them by the number of edges, faces, or vertices as well as the types of faces. Students recognize volume as an attribute of three-dimensional space. They understand that they can quantify volume by finding the total number of same-sized units of volume that they need to fill the space without gaps or overlaps. They understand that a cube that is 1 unit on an edge is the standard unit for measuring volume. They select appropriate units, strategies, and tools for solving problems that involve estimating or measuring volume. They decompose three-dimensional shapes and find surface areas and volumes of prisms. As they work with surface area, they find and justify relationships among the formulas for the areas of different polygons. They measure necessary attributes of shapes to use area formulas to solve problems.