A quadrilateral is a flat shape with four straight sides.

• Square
• Rectangle
• Parallelogram
• Rhombus
• Trapezium

## Difference between square and rhombus

 A square has got 4 sides of equal length and 4 right angles (right angle = 90 degrees). A Rhombus has got 4 sides of equal length and opposite sides are parallel and angles are equal.

## Difference between rectangle and parallelogram

 The rectangle (oblong) contains  4 right angles (an angle of 90˚). It has got 2 pairs of equal sides and 4 right angles A parallelogram is a rectangle that has been pushed over. Opposite sides are the same length and they are parallel.

Area of square  =  4a

Area of rectangle  =  Length x width

Area of parallelogram  =  base x height

Area of rhombus  =  (1/2) x (d₁ x d₂)

Area of trapezium  =  (1/2) x h (a+ b)

## Area of quadrilaterals - Example problems

Example 1 :

A window shaped like a parallelogram has an area of 18 ⅓  square feet. The height of the window is 3 ⅓ feet. How long is the base of the window?

Solution :

Area of the parallelogram  =  base x height

Area of window  =  18 ⅓  square feet

height of window  =  3 ⅓

Let "x" be the base of the parallelogram

x 3 ⅓  =  18 ⅓

x 10/3  =  55/3

x  =  (55/3) x (3/10)

x  =  11/2

x  =  5 ½ feet

Hence, the length of window is ½ feet.

Example 2 :

A section in a stained glass window is shaped like a trapezoid. The top base is 4 centimeters and the bottom base is 2.5 centimeters long. If the area of the section of glass is 3.9 square centimeters, how tall is the section?

Solution :

Area of the trapezoid  =  (1/2) x h (a + b)

length of top base (a)  =  4 cm

length of bottom base  =  2.5 cm

Area of the section  =  3.9 square centimeters

(1/2) x h (4 + 2.5)  =  3.9

(1/2) x h (6.5)  =  3.9

h  =  (3.9 x 2) / 6.5

h  =  1.2 cm

Example 3 :

A parallelogram-shaped field in a park needs sod. The parallelogram has a base of 21.5 meters and a height of 18 meters. The sod is sold in pallets of 50 square meters. How many pallets of sod are needed to fill the field?

Solution :

Base length of the park = 21.5 m

height = 18 m

Area of parallelogram shaped field = base x height

=  21.5 x 18

=  387

Number of pallets required to fill the field  =  387/50

=  7.74

Hence 8 pallets are needed to fill the field.

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