Grade 3 Math: Quadrilaterals

It was the annual Shape City Festival in Mathopolis, and all the shapes were getting ready for the grand parade. The Quadrilaterals, led by Squarey the Square, were particularly excited. Squarey, the most symmetrical and equal-sided shape in Mathopolis, was known for his love of right angles and four equal sides. His friends, Recty the Rectangle and Polly the Parallelogram, joined him in the parade. Recty had two pairs of equal sides, while Polly had opposite sides that were parallel.

The sun was shining brightly as the parade began. The Quadrilaterals marched proudly, showcasing their unique properties. Squarey was beaming with pride, showing off his four right angles to the cheering crowd. Recty elegantly displayed his two pairs of equal sides, while Polly gracefully demonstrated her parallel sides.

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Quadrilaterals are polygons with four sides. They come in various forms, each with distinct characteristics. Let’s explore the properties of squares, rectangles, and parallelograms in more detail.

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| **Shape** | **Number of Sides** | **Number of Right Angles** | **Equal sides** | **Parallel sides** |
|—————–|———————|—————————-|—————–|——————–|
| Square | 4 | 4 | 4 | 4 |
| Rectangle | 4 | 4 | 2 | 0 |
| Parallelogram | 4 | 0 | 0 | 2 |

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In a square, all four sides are equal in length, and all four angles are right angles. Rectangles have two pairs of equal sides and four right angles. Parallelograms have opposite sides that are parallel but do not necessarily have equal sides or right angles.

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A square is a special type of quadrilateral where all sides are equal, and all angles are right angles. If each

side of a square is of length \(s\), then:
– The perimeter of a square is \(4s\).
– The area of a square is \(s^2\).

Let’s say a square has a side length of \(5\) units.
– Its perimeter would be \(4 \times 5 = 20\) units.
– The area would be \(5^2 = 25\) square units.

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Rectangles have two pairs of equal sides and four right angles. If the length of the rectangle is \(l\) and the width is \(w\), then:
– The perimeter of a rectangle is \(2l + 2w\).
– The area of a rectangle is \(l \times w\).

Consider a rectangle with length \(6\) units and width \(4\) units.
– The perimeter would be \(2 \times 6 + 2 \times 4 = 12 + 8 = 20\) units.
– The area would be \(6 \times 4 = 24\) square units.

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Parallelograms have opposite sides that are parallel. If the base of a parallelogram is \(b\) and the height is \(h\), then:
– The perimeter of a parallelogram is \(2(b + h)\).
– The area of a parallelogram is \(b \times h\).

Imagine a parallelogram with a base of \(7\) units and a height of \(3\) units.
– The perimeter would be \(2(7 + 3) = 2 \times 10 = 20\) units.
– The area would be \(7 \times 3 = 21\) square units.

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– Confusing rectangles with squares: Remember, all sides of a square are equal, while rectangles have two pairs of equal sides.
– Misidentifying parallelograms: Parallelograms have opposite sides that are parallel, but not necessarily equal sides or right angles.

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In conclusion, quadrilaterals are fascinating shapes with distinct properties. Squares have four equal sides and right angles, rectangles have two pairs of equal sides and right angles, and parallelograms have opposite sides that are parallel. Understanding these properties helps us identify and differentiate between these special shapes during the Shape City Festival parade.

Now, as the Quadrilaterals continue to march proudly in the parade, children in the crowd cheer and learn about the amazing world of shapes that surrounds them.