Area of quadrilaterals :
A quadrilateral is a flat shape with four straight sides.
Types of quadrilaterals :
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.
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)
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?
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 x 3 ⅓ = 18 ⅓
x x 10/3 = 55/3
x = (55/3) x (3/10)
x = 11/2
x = 5 ½ feet
Hence, the length of window is 5 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?
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?
Base length of the park = 21.5 m
height = 18 m
Area of parallelogram shaped field = base x height
= 21.5 x 18
Number of pallets required to fill the field = 387/50
Hence 8 pallets are needed to fill the field.
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