in the given figure ABCD is a trapezium with DC=12cm and BC=40cm,angle BCD=120.find the area of the trapezium
Answers
Area of a trapezium ABCD = {¹/₂ × (AB + DC) × h} square units.
Proof: 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)
Formula of Area of a trapezium = ¹/₂ × (sum of parallel sides) × (distance between them)
Solved Examples of Area of a Trapezium
1. Two parallel sides of a trapezium are of lengths 27 cm and 19 cm respectively, and the distance between them is 14 cm. Find the area of the trapezium.
Solution:
Area of the trapezium
= ¹/₂ × (sum of parallel sides) × (distance between them)
= {¹/₂ × (27 + 19) × 14} cm²
= 322 cm²
Step-by-step explanation:
the given figure ABCD is a trapezium with DC=12cm and BC=40cm,angle BCD=120.find the area of the trapeziumstepbi cu ecpla