Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.
What to Focus On
Core idea:A basic shape is named by counting its straight sides and corners, not by how round or pointy it seems.
Common stuck point:The procedure for basic shapes is the easy part; the trap is naming a shape by how it looks rather than its sides. Asking "Can I name this figure just by counting its straight sides and corners?" first is what keeps a correct-looking calculation from being attached to the wrong concept.
Sense of Study hint:Ask: Can I name this figure just by counting its straight sides and corners?
Worked Examples
Example 1
easy
How many sides and corners does a rectangle have?A rectangle: 4 sides, 4 right-angle corners
Answer
A rectangle has 4 sides and 4 corners.
First step
1
Step 1: A rectangle is a closed 2D figure. Count its sides by tracing around it: top, right, bottom, left — that is 4 sides.
Full solution
2
Step 2: Each place where two sides meet is a corner. A rectangle has 4 corners.
3
Step 3: Because all corners are right angles (90°), a rectangle is a special type of quadrilateral.
Every corner of a rectangle is a right angle. Rectangles belong to the family of quadrilaterals — shapes with exactly four sides.
Example 2
medium
A triangle has 3 sides. A pentagon has 5 sides. How many more sides does a pentagon have than a triangle, and how many corners does each shape have?
Example 3
easy
The sun is in the sky. The grass is on the ground. Is the sun above or below the grass?
Example 4
easy
A bird flies in the sky. A fish swims in the water below. Is the fish above or below the bird?
Example 5
medium
A cat is on top of a table. A toy is on the floor. Is the toy above or below the cat?
Example 6
easy
A stop sign has 6 sides. Wait — count again carefully on a real stop sign. A hexagon has 6 sides. A stop sign has 8 sides. So a stop sign is NOT a hexagon. Is a honeycomb cell (6 sides) a hexagon?
Example 7
medium
A door is a rectangle. How many sides AND how many corners does the door have?
Example 8
medium
Compare a triangle and a rectangle. Which has MORE sides, and by how many?
Example 9
easy
You glue 2 triangles together along one full matching side. What 4-sided shape can you make?
Example 10
medium
Two squares of the same size are placed side by side, touching along one full side. What 4-sided shape is made?
Example 11
hard
You build a hexagon by joining 6 small triangles, all meeting at the center. How many triangles did you use, and how many sides does the outside of the hexagon have?
Example 12
easy
A bread loaf is cut into 3 equal slices. What is each slice called as a fraction of the loaf?
Example 13
medium
A shape has all sides the same length and 5 corners. What attribute words best describe it: regular or irregular, and what is the shape called?Regular pentagon: all sides equal, all angles equal (108° each)
Example 14
hard
You partition a rectangle into 2 equal rows. Then you partition each row into 3 equal columns. How many equal parts are there in total, and what fraction of the rectangle is each part?
Practice Problems
Try these problems on your own first, then open the solution to compare your method.
Example 1
easy
Which shape has exactly 3 sides: square, triangle, or hexagon?
Example 2
hard
A shape has 6 equal sides and 6 equal corners. What is it called, and what is the sum of all its interior angles?Regular hexagon: 6 equal sides, each interior angle 120°, sum = 720°
Example 3
easy
How many sides does a triangle have?
Example 4
easy
Which shape has no corners and no straight sides?
Example 5
easy
A shape has 4 sides that are all the same length and 4 square corners. What is it?4 equal sides + 4 right-angle corners = square
Example 6
easy
Is a shape with one curved side and no corners open or closed?
Example 7
easy
How many corners does a rectangle have?A rectangle has 4 corners, each a right angle
Example 8
easy
Which is the odd one out: square, rectangle, triangle, rhombus?
Example 9
easy
What do you call a shape with 6 sides?
Example 10
easy
True or false: every square is also a rectangle.
Example 11
medium
A shape has 4 equal sides but its corners are not right angles. What is it?4 equal sides, no right angles — a rhombus
Example 12
medium
I have 4 sides. Exactly one pair of my sides is parallel. What shape am I?Exactly one pair of parallel sides — a trapezoid
Example 13
medium
A pentagon and a triangle are placed side by side. How many sides do they have in total?
Example 14
medium
Which has more corners: two triangles or one rectangle?
Example 15
medium
You cut one square corner-to-corner with a straight line. What two shapes do you get?A diagonal cut corner-to-corner produces 2 triangles
Example 16
medium
A shape has all sides equal and all corners equal. It has 5 sides. What is it called?
Example 17
medium
Sort these by number of sides, fewest first: octagon, triangle, hexagon, square.
Example 18
medium
Which statement is always true? (a) A rectangle has 4 equal sides. (b) A square has 4 right angles.
Example 19
challenge
Two identical equilateral triangles are glued along one full side. What shape results, and how many sides does its outline have?Two equilateral triangles joined along one side form a rhombus with 4 equal sides
Example 20
challenge
A shape is a quadrilateral, every angle is a right angle, and one diagonal splits it into two congruent triangles whose legs are unequal. What shape is it, and why isn't it a square?
Example 21
challenge
How many triangles can you count in a square that has both of its diagonals drawn?
Example 22
challenge
Every regular polygon shares one property no matter how many sides it has. Name it, and explain what happens to a regular polygon's appearance as the number of sides grows very large.
Example 23
easy
Which shape is round like a ball? circle, square, or triangle?
Example 24
easy
A shape has 3 pointy corners. Is it a circle, a square, or a triangle?
Example 25
easy
A door is shaped like which one? circle, square, or rectangle-like shape with 4 corners?
Example 26
medium
A pizza slice is shaped like which one? circle, square, or triangle?
Example 27
medium
A wheel rolls because it is shaped like a what?
Example 28
medium
A book cover has 4 straight sides that are the same size. What shape is it?
Example 29
hard
Point to the shape with no corners: circle, square, or triangle?
Example 30
easy
How many sides does a rectangle have?Trace all 4 sides of a rectangle
Example 31
easy
How many corners does a hexagon have?
Example 32
easy
Your right hand is the hand you write with (for most kids). If you face the page, the door behind you is on which side: left or right?
Example 33
easy
How many sides does a triangle have? Count them.
Example 34
medium
You are facing the front of the room. The window is on your right. You turn around. Is the window now on your left or your right?
Example 35
medium
A shape has 6 sides. What is the name of the shape?
Example 36
hard
A hexagon has 6 corners. A square has 4 corners. How many corners do they have together?
Example 37
easy
Which shape has exactly 4 sides: triangle, square, or hexagon?The shape with exactly 4 sides is the square
Example 38
easy
A pizza is cut into 2 equal pieces. Each piece is called a what?
Example 39
easy
A square is cut into 4 equal pieces. Each piece is called a what?
Example 40
easy
Which shape has more sides: a triangle or a hexagon?
Example 41
medium
Sort by number of sides, fewest first: hexagon, triangle, square.
Example 42
easy
A shape has 5 sides. What is it called?A 5-sided shape is called a pentagon
Example 43
easy
A shape has 8 sides. What is it called?An 8-sided shape is called an octagon
Example 44
easy
A shape has 4 sides, 4 right-angle corners, but the long sides and short sides are different. Is it a square or a rectangle?4 right angles + unequal sides = rectangle, not a square
Example 45
easy
A rectangle is partitioned into 4 equal rows. Each row is what fraction of the rectangle?
Example 46
medium
A pentagon and an octagon are sitting together. How many sides do they have in total?