Question

Find the area of given figure $ABCDEFGH$ as per dimensions given in it.

Answer 1

In the right triangle $\Delta ABC$,
We have, from the Pythagoras theorem, $A{B}^2=B{C}^2+A{C}^2$
$\Rightarrow (5{)}^2=(4{)}^2+A{C}^2$
$\Rightarrow 25=16+A{C}^2$
$A{C}^2=25-16=9=(3{)}^2$
$\therefore AC=3cm$
$\therefore AD=AC+CD=3+4=7cm$ and also
$\therefore BG=BC+CF+FG=4+8+4=16cm$
$AH=DE=8cm$
$\text{Now area of rect. CDEF}=CD\times DF$
$=8\times 4=32c{m}^2$
$\text{and area of trapezium ABGH}=\frac{1}{2}(AH+BG)\times AC=\frac{1}{2}\times (8+16)\times 3c{m}^2=\frac{1}{2}\times 24\times 3=36c{m}^2\therefore \text{Total area of the figure}=\text{area of trapezium ABGH}+\text{area of rect. CDEF}=32+36=68c{m}^2$