Find the area of the trapezium ABCD where AB= 24 cm BC= 6cm CD= 14 cm and DA= 8cm
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Answer:
Given: AB= 24 cm BC= 6cm CD= 14 cm and DA= 8cm
To find: Area of trapezium ABCD
Step-by-step explanation:
Construction: Draw lineDE ⊥ AB and line EC⊥AB,
(For diagram see the attachment)
now from CD = FE = 14,
In right ∠d Δ BEC,
(BC)²=(BE)² + (EC)²
6²= a²+b² ______(I)
where BE=b and EC=a= FD =height
In right ∠d ΔAFD,
(AD)²= (AF)² + (FD)²
8²= (10 - b)² + a²
64 = 100 - 20b +b² +a²
20b = 100 +36 - 64 .............[from equation(I) b² +a²=36]
b = 72÷ 20
b = 3.6
36 = a² + (3.6)²
a²= 36 - 12.96
a = √23.04 = 4.8
now we have height = a = 4.8
Area of trapezium = (AB + CD) × h/2
= (24 + 14) × 4.8/2
= 36 ×2.4
=86.4 sq.cm.
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