Question

Given equilateral $ABCD$ with right angles in $B$ and $D$. We also know that $BC=1,CD=4$ and $DA=3units$. What is the area of $ABCD$

Answer 1

Length of $AE=1$

$\therefore l\left(DE\right)=3-1=2$

$\therefore l\left(CE\right)=\sqrt{16+4}=\sqrt{20}$

$\therefore$ Area of $\square ABCE=\left(1\right)\left(\sqrt{20}\right)=\sqrt{20}unit{s}^2$

$=2\sqrt{5}unit{s}^2$

$\therefore$ Area of $\Delta CDE=\frac{1}{2}\times \left(4\right)\left(2\right)$

$=4unit{s}^2$

$\therefore$ Area of $\square ABCD=(4+2\sqrt{5})unit{s}^2$