Find the area of given figure ABCDEFGH as per dimensions given in… - Vidyadip

Question

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

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Answer

In the right $\triangle ABC$,
$AB^2=BC^2+AC^2$
$\Rightarrow(5)^2=(4)^2+AC^2$
$25=16+AC^2$
$AC^2=25-16=9=(3)^2$
$AC=3 cm$
$\therefore AD=AC+CD=3+4=7 cm$
$BG=BC+CF+FG$
$=4+8+4=16$
$AH=DE=8 cm$
Now area of rectangle CDEF,
$=8 \times 4=32 cm^2$
And area of rectangle $A B G H$,
$=\frac{1}{2}(AH+BG) \times AC$
$=\frac{1}{2} \times(8+16) \times 3 cm^2$
$=\frac{1}{2} \times 24 \times 3=36 cm^2$
$\therefore$ Total area of the figure,
$=32+36$
$=68 cm^2$

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