Question

1)
ABCD is a trapezium
AB = 7, BC = 12, observe
the figure and find FC.
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Answer 1

According to the question

ABCD is a trapezium

AB = 7, BC = 12

we have to determine FC = FE+ED+DC

first of all

ED= AB because AB and ED are opposite side and by the property of trapezium, these two sides are equal so

ED = 7 cm

• as angle DBC = 60°

sin 60° = DC/ BC = DC/ 12

so, DC = 10.4 cm.

• Cos 60° = BC/BD = 12/BD

so,BD = 6

EA= BD because BD and EA are opposite side and by the property of trapezium, these two sides are equal so

EA= 6 cm

as angle AFE = 45°

tan 45° = AF/EF = 6/ EF

so, EF= 6

finally FC = FE+ED+DC = 6+7+10.5 = 23.5 cm