Question

Calculate the area of a quadrilateral given in the figures :

Answer 1

Area $\left(\Delta ABC\right)=\frac{1}{2}bh=\frac{1}{2}\times 9\times 12=54c{m}^2$

$A{C}^2=A{B}^2+B{C}^2$ [Pythagoras Theorem]

$A{C}^2=144+81$

$A{C}^2=225$

$AC=15$

$C{D}^2=A{D}^2-A{C}^2$ [Pythagoras Theorem]

$C{D}^2=289-225$

$C{D}^2=64$

$CD=8$

Area $\left(\Delta ACD\right)=\frac{1}{2}\times bh=\frac{1}{2}\times 8\times 15=60c{m}^2$

Total Area = $114c{m}^2$.