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 $\angle$DEF=$\angle$EFG=90${}^{\circ }$, then find the area of trapezium DEFG

• A. 18 cm²
• B. 16 cm²
• C. 15 cm²
• D. 20 cm²

Answer 1

The correct option is A 18 cm²

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

$\Delta$DXG is right angled triangle.

Hence, (k + 1)${}^2$ – (k – 1)${}^2$ = 4${}^2$

Hence, k = 4 and so GF = 6 cm

Area of trapezium DEFG = $\frac{(3+6)}{2}$ * 4 = 18 cm${}^2$