Geometric Trapezium Problem Solving

Question

A trapezium $ABCD$ is split into four identical trapezia as shown below.

Given that $AB$ has length $6$ cm, find the area of $ABCD$.

My answer was $27\sqrt{3}\ cm = 46.77\ cm(2 d.p.)$

What do you guys think?

Answer 1

It seems correct, indeed the trapezoid is an half hexagon since

$$\angle D=\angle A \quad \angle B=\angle C=2\angle A \implies6\angle A=360° \implies\angle A=60°$$

then

• $AD=2AB=12 cm$
• $H=6\sqrt 3 /2=3 \sqrt 3$

and therefore

$$A=\frac12 (AD+BC)H=27\sqrt 3$$