Question
A trapezium DEFG is circumscribed about a circle that has centre C and radius 2 cm. If DE = 3 cm and the measure of∠DEF=∠EFG=90∘, then find the area of trapezium DEFG
Answer: Option A
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A
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A
Draw perpendicular from D to GF meeting at X.
Also, let GN = GP = k
Since, DE = XF = 3 cm
NX = 3 – 2 = 1 = DM = DP
Therefore, GX = k – 1
ΔDXG is right angled triangle.
Hence, (k + 1)2 – (k – 1)2 = 42
Hence, k = 4 and so GF = 6 cm
Area of trapezium DEFG = (3+6)2 * 4 = 18 cm2
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