Square Practice Problems for 9th Grade - Geometry Worksheets

Master square properties, area calculations, and proofs with interactive practice problems designed for 9th grade geometry students. Build confidence with step-by-step solutions.

📚Practice Square Properties and Calculations

Calculate square area using the formula A = a²
Identify and apply all five key properties of squares
Prove that a quadrilateral is a square using systematic steps
Distinguish between squares, rectangles, rhombuses, and parallelograms
Solve problems involving square diagonals and their perpendicular intersection
Apply square properties to solve real-world geometry problems

Understanding Square for 9th Grade

Complete explanation with examples

What is a square?

A quadrilateral whose sides (or edges) are all equal and all its angles are also equal, is a square.
Furthermore, a square is a combination of a parallelogram, a rhombus, and a rectangle.
Therefore, the square has all the properties of the parallelogram, the rhombus, and the rectangle.

Square

Detailed explanation

Practice Square for 9th Grade

Test your knowledge with 27 quizzes

Look at the square below:

What is its area?

Examples with solutions for Square for 9th Grade

Step-by-step solutions included

Exercise #1

Look at the square below:

What is the area of the square?

Step-by-Step Solution

Remember that the area of the square is equal to the side of the square raised to the second power

The formula for the area of the square is:

$A=L^2$

We calculate the area of the square:

$A=40^2=1600$

Answer:

$1600$

Video Solution

Exercise #2

Look at the square below:

What is the area of the square?

Step-by-Step Solution

The area of the square is equal to the side of the square raised to the second power.

That is:

$A=L^2$

Since the drawing gives us one side of the square, and in a square all sides are equal, we will solve the area of the square as follows:

$A=2^2=4$

Answer:

$4$

Video Solution

Exercise #3

Look at the square below:

What is the area of the square?

Step-by-Step Solution

The area of the square is equal to the side of the square raised to the second power.

That is:

$A=L^2$

Since the drawing gives us one side of the square, and in a square all sides are equal, we will solve the area of the square as follows:

$A=10^2=100$

Answer:

$100$

Video Solution

Exercise #4

Look at the square below:

What is the area of the square?

Step-by-Step Solution

The area of the square is equal to the side of the square raised to the second power.

That is:

$A=L^2$

Since the drawing gives us one side of the square, and in a square all sides are equal, we will solve the area of the square as follows:

$A=11^2=121$

Answer:

$121$

Video Solution

Exercise #5

Look at the square below:

What is the area of the square?

Step-by-Step Solution

The area of the square is equal to the side of the square raised to the second power.

That is:

$A=L^2$

Since the drawing gives us one side of the square, and in a square all sides are equal, we will solve the area of the square as follows:

$A=12^2=144$

Answer:

$144$

Video Solution

Frequently Asked Questions

Everything you need to know about Square for 9th Grade

What is the formula for finding the area of a square?

The area of a square is calculated using the formula A = a², where 'a' represents the length of one side. Since all sides of a square are equal, you simply multiply one side by itself to find the total area.

What are the 5 main properties of a square?

The five key properties of a square are: 1) All sides are equal in length, 2) All angles measure 90 degrees, 3) Two pairs of opposite sides are parallel, 4) Diagonals intersect perpendicularly and are equal in length, 5) Diagonals bisect each other at right angles.

How do you prove a quadrilateral is a square step by step?

To prove a quadrilateral is a square, follow these three steps: First, prove it's a parallelogram using properties like opposite sides being parallel or equal. Second, prove the parallelogram is either a rectangle or rhombus. Third, prove the rectangle or rhombus is a square using specific conditions like equal adjacent sides or perpendicular diagonals.

What's the difference between a square and a rectangle?

While every square is a rectangle, not every rectangle is a square. A rectangle has four right angles and opposite sides are equal, but adjacent sides can be different lengths. A square has all the properties of a rectangle plus all four sides are equal in length.

How do you prove a rhombus is a square?

To prove a rhombus is a square, you need to show one of these conditions: either the rhombus has at least one right angle (90 degrees), or the diagonals of the rhombus are equal in length. Meeting either condition confirms the rhombus is actually a square.

What makes square diagonals special in geometry?

Square diagonals have three unique properties: they are equal in length, they intersect at right angles (perpendicular), and they bisect each other. This means the diagonals cut each other exactly in half and form four right angles at their intersection point.

Is every square also a parallelogram and rhombus?

Yes, every square is both a parallelogram and a rhombus. A square inherits all properties from these shapes: parallel opposite sides (parallelogram), equal sides (rhombus), plus its own unique property of having all right angles.

How do you find the side length of a square if you know the area?

If you know the area of a square, find the side length by taking the square root of the area. Since A = a², then a = √A. For example, if the area is 36 square units, the side length is √36 = 6 units.

Practice by Question Type

Choose your preferred learning style and practice format for fraction problems

Increasing a specific element by addition of.....or multiplication by....... Worded problems True / false Express using Applying the formula Calculate The Missing Side based on the formula Properties of triangles within a square Finding the size of angles in a triangle Parallelogram within a square Determine whether the quadrilateral is a square True / false

Square Practice Problems for 9th Grade - Geometry Worksheets

Understanding Square for 9th Grade

What is a square?

Square

Practice Square for 9th Grade

Examples with solutions for Square for 9th Grade

Frequently Asked Questions

What is the formula for finding the area of a square?

What are the 5 main properties of a square?

How do you prove a quadrilateral is a square step by step?

What's the difference between a square and a rectangle?

How do you prove a rhombus is a square?

What makes square diagonals special in geometry?

Is every square also a parallelogram and rhombus?

How do you find the side length of a square if you know the area?

More Square for 9th Grade Questions

Area of the Square

Properties, Characteristics and proofs

Practice by Question Type

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