Rectangles for Ninth Grade - Examples, Exercises and Solutions

Practice RectanglePractice From a Quadrilateral to a RectanglePractice From a Parallelogram to a Rectangle
Question Types:
Area of a Rectangle: Applying the formulaArea of a Rectangle: A shape consisting of several shapes (requiring the same formula)Area of a Rectangle: Calculate The Missing Side based on the formulaArea of a Rectangle: Calculation using the diagonalArea of a Rectangle: Extended distributive lawArea of a Rectangle: Finding Area based off Perimeter and Vice VersaArea of a Rectangle: Subtraction or addition to a larger shapeArea of a Rectangle: Using additional geometric shapesArea of a Rectangle: Using Pythagoras' theoremArea of a Rectangle: Using ratios for calculationArea of a Rectangle: Using short multiplication formulasArea of a Rectangle: Using variablesArea of a Rectangle: Worded problemsCharacteristics and Proofs of a Rectangle: Drawing a rectangle based on propertiesCharacteristics and Proofs of a Rectangle: Identifying and defining elementsCharacteristics and Proofs of a Rectangle: True / false

Properties of a Rectangle

A rectangle is a quadrilateral with two pairs of parallel opposite edges (sides), the angles of which all equal 90 degrees.

B- Properties of a Rectangle
  1. The pairs of sides in a rectangle are opposite, equal, and parallel.
  2. Each of the angles in a rectangle are equal to 90 degrees.
  3. The diagonals of a rectangle are equal.
  4. The diagonals of a rectangle intersect and do so at the midpoint of each other.
  5. Since the diagonals are equal, so are their halves.

Note:
The diagonals of a rectangle are not perpendicular (they are oblique) and do not cross the angles of the rectangle.

Detailed explanation

Practice Rectangles for Ninth Grade

Question 1

Look at the rectangle below.

Side AB is 2 cm long and side BC has a length of 7 cm.

What is the perimeter of the rectangle?
222777AAABBBCCCDDD

Question 2

Look at rectangle ABCD below.

Side AB is 10 cm long and side BC is 2.5 cm long.

What is the area of the rectangle?
1010102.52.52.5AAABBBCCCDDD

Question 3

Given the following rectangle:

111111777AAABBBDDDCCC

Find the area of the rectangle.

Question 4

Given the following rectangle:

222555AAABBBDDDCCC

Find the area of the rectangle.

Question 5

Given the following rectangle:

888444AAABBBDDDCCC

Find the area of the rectangle.

Examples with solutions for Rectangles for Ninth Grade

Exercise #1

Look at the rectangle below.

Side AB is 2 cm long and side BC has a length of 7 cm.

What is the perimeter of the rectangle?
222777AAABBBCCCDDD

Video Solution

Step-by-Step Solution

Given that in a rectangle every pair of opposite sides are equal to each other, we can state that:

AB=CD=2 AB=CD=2

AD=BC=7 AD=BC=7

Now we can add all the sides together and find the perimeter:

2+7+2+7=4+14=18 2+7+2+7=4+14=18

Answer

18 cm

Exercise #2

Look at rectangle ABCD below.

Side AB is 10 cm long and side BC is 2.5 cm long.

What is the area of the rectangle?
1010102.52.52.5AAABBBCCCDDD

Video Solution

Step-by-Step Solution

Let's begin by multiplying side AB by side BC

If we insert the known data into the above equation we should obtain the following:

10×2.5=25 10\times2.5=25

Thus the area of rectangle ABCD equals 25.

Answer

25 cm²

Exercise #3

Given the following rectangle:

111111777AAABBBDDDCCC

Find the area of the rectangle.

Video Solution

Step-by-Step Solution

Let's calculate the area of the rectangle by multiplying the length by the width:

11×7=77 11\times7=77

Answer

77

Exercise #4

Given the following rectangle:

222555AAABBBDDDCCC

Find the area of the rectangle.

Video Solution

Step-by-Step Solution

Let's calculate the area of the rectangle by multiplying the length by the width:

2×5=10 2\times5=10

Answer

10

Exercise #5

Given the following rectangle:

888444AAABBBDDDCCC

Find the area of the rectangle.

Video Solution

Step-by-Step Solution

Let's calculate the area of the rectangle by multiplying the length by the width:

4×8=32 4\times8=32

Answer

32

Question 1

Look at the rectangle ABCD below.

Given in cm:

AB = 10

BC = 5

Calculate the area of the rectangle.

101010555AAABBBCCCDDD

Question 2

ABCD is a rectangle.

Given in cm:

AB = 7

BC = 5

Calculate the area of the rectangle.

777555AAABBBCCCDDD

Question 3

True or false?

One of the angles in a rectangle may be an acute angle.

Question 4

Look at the rectangle ABCD below.

Side AB is 6 cm long and side BC is 4 cm long.

What is the area of the rectangle?
666444AAABBBCCCDDD

Question 5

Look at the rectangle below.

Side DC has a length of 1.5 cm and side AD has a length of 9.5 cm.

What is the perimeter of the rectangle?

1.51.51.5AAABBBCCCDDD9.5

Exercise #6

Look at the rectangle ABCD below.

Given in cm:

AB = 10

BC = 5

Calculate the area of the rectangle.

101010555AAABBBCCCDDD

Video Solution

Step-by-Step Solution

Let's calculate the area of the rectangle by multiplying the length by the width:

AB×BC=10×5=50 AB\times BC=10\times5=50

Answer

50

Exercise #7

ABCD is a rectangle.

Given in cm:

AB = 7

BC = 5

Calculate the area of the rectangle.

777555AAABBBCCCDDD

Video Solution

Step-by-Step Solution

Let's calculate the area of the rectangle by multiplying the length by the width:

AB×BC=7×5=35 AB\times BC=7\times5=35

Answer

35

Exercise #8

True or false?

One of the angles in a rectangle may be an acute angle.

Video Solution

Step-by-Step Solution

One of the properties of a rectangle is that all its angles are right angles.

Therefore, it is not possible for an angle to be acute, that is, less than 90 degrees.

Answer

False

Exercise #9

Look at the rectangle ABCD below.

Side AB is 6 cm long and side BC is 4 cm long.

What is the area of the rectangle?
666444AAABBBCCCDDD

Video Solution

Step-by-Step Solution

Remember that the formula for the area of a rectangle is width times height

 

We are given that the width of the rectangle is 6

and that the length of the rectangle is 4

 Therefore we calculate:

6*4=24

Answer

24 cm²

Exercise #10

Look at the rectangle below.

Side DC has a length of 1.5 cm and side AD has a length of 9.5 cm.

What is the perimeter of the rectangle?

1.51.51.5AAABBBCCCDDD9.5

Video Solution

Step-by-Step Solution

Since in a rectangle every pair of opposite sides are equal to each other, we can state that:

AD=BC=9.5 AD=BC=9.5

AB=CD=1.5 AB=CD=1.5

Now we can add all the sides together and find the perimeter:

1.5+9.5+1.5+9.5=19+3=22 1.5+9.5+1.5+9.5=19+3=22

Answer

22 cm

Question 1

The width of a rectangle is equal to 15 cm and its length is 3 cm.

Calculate the area of the rectangle.

Question 2

Look at the rectangle ABCD below.

Side AB is 4.5 cm long and side BC is 2 cm long.

What is the area of the rectangle?
4.54.54.5222AAABBBCCCDDD

Question 3

True or false:

The sum of the angles of a rectangle is 360.

Question 4

Given the following rectangle:

666999AAABBBDDDCCC

Find the area of the rectangle.

Question 5

Look at the parallelogram ABCD below.

AAABBBDDDCCC

What can be said about triangles ACD and ABD?

Exercise #11

The width of a rectangle is equal to 15 cm and its length is 3 cm.

Calculate the area of the rectangle.

Video Solution

Step-by-Step Solution

To calculate the area of the rectangle, we multiply the length by the width:

15×3=45 15\times3=45

Answer

45

Exercise #12

Look at the rectangle ABCD below.

Side AB is 4.5 cm long and side BC is 2 cm long.

What is the area of the rectangle?
4.54.54.5222AAABBBCCCDDD

Video Solution

Step-by-Step Solution

We begin by multiplying side AB by side BC

We then substitute the given data and we obtain the following:

4.5×2=9 4.5\times2=9

Hence the area of rectangle ABCD equals 9

Answer

9 cm²

Exercise #13

True or false:

The sum of the angles of a rectangle is 360.

Step-by-Step Solution

We know that the sum of the angles in a quadrilateral is 360.

Since a rectangle is a type of quadrilateral, the sum of its angles is also equal to 360.

Likewise, we know that all the angles in a rectangle are right angles (90 degrees).

90×4=360 90\times4=360

Answer

True

Exercise #14

Given the following rectangle:

666999AAABBBDDDCCC

Find the area of the rectangle.

Video Solution

Step-by-Step Solution

We will use the formula to calculate the area of a rectangle: length times width

9×6=54 9\times6=54

Answer

54

Exercise #15

Look at the parallelogram ABCD below.

AAABBBDDDCCC

What can be said about triangles ACD and ABD?

Video Solution

Step-by-Step Solution

According to the side-angle-side theorem, the triangles are similar and coincide with each other:

AC = BD (Any pair of opposite sides of a parallelogram are equal)

Angle C is equal to angle B.

AB = CD (Any pair of opposite sides of the parallelogram are equal)

Therefore, all of the answers are correct.

Answer

All answers are correct.

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