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Here you will learn about rectangles, including how to identify a rectangle, the properties of a rectangle, and how to find the area of a rectangle and the perimeter of a rectangle.
Students will first learn about rectangles as part of geometry in 1 st grade and will expand upon their knowledge of rectangles throughout the elementary grades.
A rectangle is a type of quadrilateral, which is a polygon with 4 sides. The word rectangle comes from the Latin rectus (or rect) meaning “right” or “straight” and angulus meaning “angle.” A rectangle is also a parallelogram since it has 2 pairs of parallel sides.
The opposite sides of a rectangle are of equal length. A rectangle also has 4 congruent interior angles, all of which are 90^{\circ} , or right angles. A rectangle also has 4 vertices, which are the corners of the rectangle.
Beginning in 3 rd grade, students will learn to find the area and perimeter of a rectangle.
To find the area of a rectangle, you multiply its length by its width. To find the perimeter of a rectangle, you add up all of its side lengths.
For example,
Area of a rectangle | Perimeter of a rectangle |
---|---|
![]() \begin{aligned} \text { Area } & =\text { length } \times \text { width } \\ & =5 \mathrm{ft} \times 8 \mathrm{ft} \\ & =40 \mathrm{ft}^2 \end{aligned} | ![]() \begin{aligned} \text { Perimeter } & =8 \mathrm{ft}+5 \mathrm{ft}+8 \mathrm{ft}+5 \mathrm{ft} \\ & =26 \mathrm{ft} \end{aligned} |
How does this relate to 1 st grade math through 5 th grade math?
In order to identify a rectangle:
Assess math progress for the end of grade 4 and grade 5 or prepare for state assessments with these mixed topic, multiple choice questions and extended response questions!
DOWNLOAD FREEAssess math progress for the end of grade 4 and grade 5 or prepare for state assessments with these mixed topic, multiple choice questions and extended response questions!
DOWNLOAD FREEIs this shape a rectangle?
A rectangle has 4 sides, 4 right angles, 2 pairs of parallel sides, and 2 pairs of opposite sides that are of equal length.
2State whether or not the shape is a rectangle.
This shape is a rectangle.
Is this shape a rectangle?
Look for the characteristics of a rectangle.
A rectangle has 4 sides, 4 right angles, 2 pairs of parallel sides, and 2 pairs of opposite sides that are of equal length.
State whether or not the shape is a rectangle.
This shape is a rectangle. It is also a square since it has 4 equal sides.
Is this shape a rectangle?
Look for the characteristics of a rectangle.
A rectangle has 4 sides, 4 right angles, 2 pairs of parallel sides, and 2 pairs of opposite sides that are of equal length.
State whether or not the shape is a rectangle.
This shape is not a rectangle.
If the shape is not a rectangle, explain what characteristics are different.
This shape does not have 4 right angles.
Henry wants to classify the shape shown below. Which of the following names can this shape be classified as?
polygon, quadrilateral, parallelogram, rectangle, trapezoid, kite, rhombus, square
Look for the characteristics of a rectangle.
A rectangle has 4 sides, 4 right angles, 2 pairs of parallel sides, and 2 pairs of opposite sides that are of equal length.
State whether or not the shape is a rectangle.
This shape is a rectangle. It is also a polygon, quadrilateral, and a parallelogram.
If the shape is not a rectangle, explain what characteristics are different.
The shape is not a trapezoid, kite, rhombus, or square.
In order to find the area of a rectangle:
Find the area of rectangle ABCD .
Determine the length and width of the rectangle.
The length of the rectangle is 9 inches and the width of the rectangle is 4 inches.
Multiply length times width.
\begin{aligned} \text {Area } & =\text { length } \times \text { width } \\\\ & =9 \times 4 \\\\ & =36 \end{aligned}
Label the area with square units.
\text {Area }=36 \text { square inches }
In order to find the perimeter of a rectangle:
Find the perimeter of the rectangle.
Determine the side lengths of the rectangle.
The side lengths are 10{~cm}, 10{~cm}, 3{~cm}, and 3{~cm} . Even though you are only given the length and width, you will use each of them twice since the opposite sides are the same length.
Add the side lengths together.
\begin{aligned} \text {Perimeter } & =10+10+3+3 \\\\ & =26 \end{aligned}
Label the perimeter with the correct units.
\text {Perimeter }= 26 \mathrm{~cm}
1) Which shape is a rectangle?
For a shape to be a rectangle, it must have 4 sides, 4 right angles, 2 pairs of parallel sides, and 2 pairs of opposite sides that are of equal length. The second shape is the only one with all of those properties.
2) Which shape is not a rectangle?
For a shape to be a rectangle, it must have 4 sides, 4 right angles, 2 pairs of parallel sides, and 2 pairs of opposite sides that are of equal length.
The last shape is the only one without all of those properties since it does not have 4 right angles.
3) What is one property of a rectangle?
opposite sides are the same length
4 equal sides
only 1 pair of parallel sides
adjacent sides are always the same length
The properties of a rectangle are: 4 sides, 4 right angles, 2 pairs of parallel sides, and 2 pairs of opposite sides that are of equal length. Their adjacent sides may sometimes be the same length, such as in a square, but not always.
4) A rectangle is also a…
square
trapezoid
right triangle
parallelogram
A rectangle is also a parallelogram because in order for a shape to be a parallelogram, it must have 4 sides and 2 pairs of parallel sides. A rectangle has both of those properties, so it is a parallelogram.
5) What is the area of the rectangle?
To find the area of a rectangle, you multiply the length of the rectangle by the width of the rectangle.
7 \mathrm{~m} \times 5 \mathrm{~m}=35 \mathrm{~m}^2
6) What is the perimeter of the rectangle?
To find the perimeter of a rectangle, you need to add up its 4 sides. There are only 2 side lengths shown, but since you know that a rectangle has opposite sides that are the same length, you know the lengths of the non-labeled sides as well.
1 \mathrm{~cm}+1 \mathrm{~cm}+9 \mathrm{~cm}+9 \mathrm{~cm}=20 \mathrm{~cm}
A rectangle is a type of quadrilateral, which is a polygon with 4 sides, that has 2 pairs of parallel sides, 4 right angles, and opposite sides that are the same length.
The properties of a rectangle are: 4 sides, 4 right angles, 2 pairs of parallel sides, and 2 pairs of opposite sides that are of equal length.
You can find the area of a rectangle by multiplying its length times its width.
Area of rectangle = length × width
You can find the perimeter of a rectangle by adding up its 4 side lengths.
Perimeter of a rectangle = sum of all its 4 sides
The length can be calculated with the pythagorean theorem, if the other two dimensions of the rectangle are known.
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