Quadrilateral: Definition, Properties, Family Tree, Formula, Examples

What Is Quadrilateral

Quadrilateral is two-dimension shape that closed and has four sides. It come from latin words, “quadri” means four and “lateral” means sides.

The internal angle is 360°. In real life, there are many things that has quadrilateral shape. For example: table top, book, picture, kite, envelope, etc.

Quadrilateral Properties

There are two of quadrilateral properties.

  1. It closed shape and has four sides
  2. Sum of all internal angles is 360°

Quadrilateral Family Tree

Quadrilateral2

Types of Quadrilateral

Quadrilateral is general form of two-dimension shape. It has five types of quadrilateral:

1. Rectangle

The specific property of rectangle is it has four right angles. Beside that, the diagonals bisect each other and the opposite sides are parallel and equal.    

Rectangle

2. Square

The specific properties of rectangle are it has four same side (the opposite sides are parallel and equal), four right angles, and the diagonals bisect each other.

Square

3. Rhombus

The properties of rhombus are all sides are equal and the opposites are parallel each other. But the angles are not 90°. It is the different property with square.

Rhombus

4. Parallelogram

The properties of parallelogram are the opposite angles are equals, the opposite sides are equal and parallel, diagonals bisect each other, and sum of two adjacent angles is 180°.

parallelogram

5. Trapezoid

It is also called as trapezium. It is quadrilateral that has one pair of parallel side. Another pair is called as lateral sides. In another words, the property of trapezoid is only one pair of parallel side that opposite each other.

Trapezoid

6. Kite

Kite has two pairs of sides. Each pair is made of two equal-length sides that join each other. The others properties of kite are the angles that two pairs meet are equal, the diagonals bisect each other and it is right angles.

Kite

Area and Perimeter of Quadrilateral

There is table of area and perimeter of quadrilateral’s formula

QuadrilateralAreaPerimeter
RectangleLength x Breadth(LxB)2x(L+B)
SquareSide x side(sxs = s2)4xs
Rhombus½ x diameter1 x diameter2(½xd1xd2)4xs
ParallelogramLength x Breadth(LxB)2x(L+B)
Trapezoid½ x sum of lengths of all parallel sides x height(½ x (AB+CD)xh)Sum of lengths of all sides(AB+BC+CD+AD)

Quadrilateral Examples

1. Dian wants to build a fence the garden that has square shape. But she wants the distance between garden and the fence is 0,5m. The side of Dian’s garden can be planted 5 trees that have 1m in distance between one tree to another. How many meters the fence that need to build?

Answer:

Based on the problem, it can be illustrated

Quadrilateral Example

The length of garden is 4m, it is because there are 5 trees and the distance one tree t another is 1m.

Because of there is distance between garden and the fence, the length of fence is

4 + 0,5 + 0,5 = 5m.

So, the fence is

4 x length of each side = 4 x 5 = 20m.

2. Steve want to paint the wall. He wants to make trapezoid shape on the wall. The wall’s size is 3×4,5m. Each trapezoid has 27cm and 15cm on the parallel sides and 10cm on the lateral sides. Determine the remainder of the wall if he wants to make a trapezoid.

Answer:

Wall’s area =3×4,5 = 13,5m2 = 1350cm2

Quadrilateral Example2

Using Pythagoras to determine the height = 8 cm

Area of trapezoid = ½ (15+27).8 = 168 cm2

So, the remainder is = 1350 – 168 = 1182 cm2