Lesson 9.3 · Perimeter and Shapes
Quadrilaterals
Squares, rectangles and many other shapes all belong to one big family: the quadrilaterals. Knowing what the members of the family share, and how they are different, helps you name any four-sided shape.
What is a quadrilateral?
"Quad" means four. A quadrilateral is a closed shape with 4 straight sides.
Definition
Quadrilateral
A quadrilateral is a closed shape with 4 straight sides and 4 angles (corners).
A right angle is a square corner, like the corner of a sheet of paper.
Some sides are parallel. Parallel sides go in the same direction and never meet, like the two rails of a train track.
Members of the family
Some quadrilaterals have special names because of their sides and angles.
| Shape | What makes it special |
|---|---|
| rectangle | 4 right angles |
| square | 4 right angles and 4 sides of the same length |
| rhombus | 4 sides of the same length |
| trapezoid | at least one pair of parallel sides |
The last shape has 4 sides, so it is a quadrilateral. But it has no right angles, no equal sides and no parallel sides, so it has no special name.
One shape, many names
A shape can belong to more than one group. Look at a square:
- It has 4 right angles, so it is a rectangle.
- It has 4 sides of the same length, so it is a rhombus.
- It has 4 sides, so it is a quadrilateral.
Shapes share attributes
Every square is a rectangle and a rhombus. Every rectangle, rhombus and trapezoid is a quadrilateral.
But not every rectangle is a square, and not every rhombus is a square.
Worked example: Name the shape
A shape has 4 sides that are all the same length. None of its angles are right angles. What is its best name?
All 4 sides are equal, so it is a rhombus. It has no right angles, so it is not a square or a rectangle.
Worked example: Is it a square?
Ava draws a rectangle that is 5 inches long and 2 inches wide. Is it a square?
No. It has 4 right angles, but its sides are not all the same length. A square needs both.
Worked example: Perimeter of a rhombus
A rhombus has one side that is 5 centimeters long. What is its perimeter?
All 4 sides of a rhombus are the same length. .
The perimeter is 20 centimeters.
Common mistake
Turning a shape does not change its name. A square turned on its point still has 4 equal sides and 4 right angles, so it is still a square, even if it looks like a diamond.
Practice
How many sides does a quadrilateral have?
Type a number.
A shape has 4 right angles and 4 sides that are all the same length. What is its best name?
Which shape is not a quadrilateral?
How many right angles does a rectangle have?
Type a number.
Which sentence is true?
Which names fit a square?
A rhombus has sides that are 7 cm long. What is its perimeter, in centimeters?
Type a number.
Liam draws a rectangle that is 8 inches long and 3 inches wide. Then he draws a square with sides that are 3 inches long. What is the total of the two perimeters, in inches?
Type a number.