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 Options: A . &nbsp18 cm2 B . &nbsp16 cm2 C . &nbsp15 cm2 D . &nbsp20 cm2

A trapezium DEFG is circumscribed about a circle that has centre C and radius

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 $^{\circ}$ , then find the area of trapezium DEFG

Options:

A . 18 cm2

B . 16 cm2

C . 15 cm2

D . 20 cm2

Answer: Option A
:
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

Δ

DXG is right angled triangle.
Hence, (k + 1)

^{2}

– (k – 1)

^{2}

= 42
Hence, k = 4 and so GF = 6 cm
Area of trapezium DEFG =

\frac{(3 + 6)}{2}

* 4 = 18 cm

^{2}

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