the area of a trapezium whose parallel sides are of lengths 40 and 24 metres and whose non parallel sides are equal , each being 10 metres is
Answers
Answer:
Area of a trapezium ABCD
= area (∆DFA) + area (rectangle DFEC) + area (∆CEB)
= (¹/₂ × AF × DF) + (FE × DF) + (¹/₂ × EB × CE)
= (¹/₂ × AF × h) + (FE × h) + (¹/₂ × EB × h)
= ¹/₂ × h × (AF + 2FE + EB)
= ¹/₂ × h × (AF + FE + EB + FE)
= ¹/₂ × h × (AB + FE)
= ¹/₂ × h × (AB + DC) square units.
= ¹/₂ × (sum of parallel sides) × (distance between them)
Step-by-step explanation:
Area of a trapezium ABCD
= area (∆DFA) + area (rectangle DFEC) + area (∆CEB)
= (¹/₂ × AF × DF) + (FE × DF) + (¹/₂ × EB × CE)
= (¹/₂ × AF × h) + (FE × h) + (¹/₂ × EB × h)
= ¹/₂ × h × (AF + 2FE + EB)
= ¹/₂ × h × (AF + FE + EB + FE)
= ¹/₂ × h × (AB + FE)
= ¹/₂ × h × (AB + DC) square units.
= ¹/₂ × (sum of parallel sides) × (distance between them)
Step-by-step explanation:
Given That
Parallel Sides of a Trapezium are 19 m and 24 m .
Distance between them is 40 m .
To Find :
Area of Trapezium .
Solution :
\longmapsto\tt{Parallel\:Sides=19\:m\:and\:24\:m}⟼ParallelSides=19mand24m
As Given that the Distance between the Parallel sides is 40 m . So ,
\longmapsto\tt{Height=40\:m}⟼Height=40m
Using Formula :
\longmapsto\tt\boxed{Area\:of\:Trapezium=\dfrac{1}{2}\times{(Sum\:of\:parallel\:Sides)}\times{h}}⟼
AreaofTrapezium=
2
1
×(SumofparallelSides)×h
Putting Values :
\longmapsto\tt{\dfrac{1}{2}\times{(19+24)}\times{40}}⟼
2
1
×(19+24)×40
\longmapsto\tt{\dfrac{1}{{\cancel{2}}}\times{43}\times{{\cancel{40}}}}⟼
2
1
×43×
40
\longmapsto\tt{43\times{20}}⟼43×20
\longmapsto\tt\bf{860\:{m}^{2}}⟼860m
2
So , The Area of Trapezium is 860 m² ...
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Trapezium
A Quadrilateral whose one pair of opposite sides are parallel is known as Trapezium .
Properties of Trapezium :
Sum of all the angles of a trapezium is 360° .
A Trapezium has two parallel and two non-parallel sides .
Diagonals of a trapezium bisects each other .