Polygons: Trapezoids, Rhombuses, and Hexagons - First Grade Mathematics

Beyond the familiar shapes of circles, triangles, and rectangles lies a marvelous family of special polygons waiting to be explored! A polygon is simply any closed 2D shape made entirely of straight line segments. In first grade, pattern block sets introduce you to three extraordinary polygons: the sturdy trapezoid, the tilted rhombus, and the six-sided hexagon. When you learn how to identify these special shapes by counting their sides and vertices, you can build intricate geometric mosaics. In this chapter, you will master trapezoids, rhombuses, and hexagons.

The Trapezoid: The Four-Sided Wedge

A trapezoid is a four-sided polygon (a quadrilateral) with a very special pair of sides.

The Trapezoid (Pattern Block: Red):
          +-------+         Short Top Side
         /         \
        +-----------+       Long Bottom Side (Both are parallel!)

Attributes of a Trapezoid:

A trapezoid has 4 straight sides and 4 vertices. Its top side and bottom side run in the exact same direction like train tracks (they are parallel), but one is shorter than the other. Its other two sides slant inward or outward. In a classroom pattern block set, the trapezoid is the red wooden block. Real-World Examples: A lampshade, a flowerpot, or the roof of a house!

The Rhombus: The Diamond Twin

Many people see a rhombus and shout: "Look, a diamond!" But in mathematics, its true name is a rhombus!

The Rhombus (Pattern Block: Blue):
           /\
          /  \       4 Straight Sides (ALL EQUAL LENGTH!)
          \  /       4 Vertices
           \/

Attributes of a Rhombus:

A rhombus is a quadrilateral with 4 straight sides of the exact same length, but unlike a square, its corners are slanted rather than square! It has two sharp, pointy acute corners and two wide obtuse corners. If you take a square made of sticks and gently push its top corner sideways, it tilts into a rhombus! In pattern block sets, the rhombus is the blue diamond block or the skinny tan block.

The Hexagon: The Wonder of Six Sides

The prefix "hexa-" means six (like a hexapod, which is an insect with six legs).

The Regular Hexagon (Pattern Block: Yellow):
          +-------+
         /         \        6 Straight Sides
        +           +       6 Vertices
         \         /
          +-------+

Attributes of a Hexagon:

A hexagon is any closed 2D shape with exactly 6 straight sides and 6 vertices. A regular hexagon has six sides of equal length and six equal angles. In pattern block sets, the hexagon is the big yellow block. Real-World Examples: Honeycomb cells built by honeybees, the ends of metal bolts, and snowflakes!

Summary of the Special Polygons

Polygon Comparison Table:
Shape Name   Sides   Vertices   Pattern Block Color
Trapezoid      4        4       Red
Rhombus        4        4       Blue / Tan
Hexagon        6        6       Yellow

Practice Exercises

Exercise 1: How many sides and vertices does a hexagon have? Name one place in nature where hexagons appear.

Exercise 2: What is the mathematical name for the shape often called a "diamond"? How many sides does it have, and what is special about the length of its sides?

Exercise 3: How many sides does a trapezoid have? Which shape family does it belong to because of its side count?

Exercise 4: Look at a yellow hexagon pattern block and a red trapezoid pattern block. How many trapezoids fit together to cover one hexagon?

Solutions and Explanations

Solution to Exercise 1: A hexagon has 6 straight sides and 6 vertices. Hexagons appear in nature in honeybee honeycombs and in snowflakes.

Solution to Exercise 2: The mathematical name is a rhombus. A rhombus has 4 straight sides, and all 4 sides are the exact same length.

Solution to Exercise 3: A trapezoid has 4 straight sides and 4 vertices. Because it has four sides, it belongs to the quadrilateral family.

Solution to Exercise 4: Exactly 2 red trapezoid pattern blocks fit together along their long bottom edges to completely cover one yellow hexagon.