Question

Find the area of the trapezium ABCD where AB= 24 cm BC= 6cm CD= 14 cm and DA= 8cm

Answer 1

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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