Question

The figure given below shows the cross-section of a concrete structure. Calculate the area of cross-section if $AB=1.8m,CD=0.6m,DE=0.8m,EF=0.3m$ and $AF=1.2m$.

• A. $2.46$ sq. m
• B. $4.7$ sq. m
• C. $1.34$ sq. m
• D. $3.14$ sq. m

Answer 1

The correct option is A $2.46$ sq. m

$AB=1.8m,CD=0.6m,DE=0.8m$
$EF=0.3m$ and $AF=1.2m$
Let $CX$ is perpendicular drawn from $C$ to $AB$,
and $EY$ is perpendicular drawn to $CX$.

Then $DEYC$ form rectangle with length $DE=YC$ and breadth $DC=EY$

Also, $AFYX$ form a rectangle with length $AF=XY$ and $AX=FY$
Now, $CX=XY+YC$
$⟹CX=AF+ED$ ..... $[\because AF=XY,DE=YC]$
$⟹CX=1.2+0.8$
$⟹CX=2m$
Again, $AB=AX+XB$
$⟹XB=AB-AX$
$⟹XB=1.8-FY$
$⟹XB=1.8-(FE+EY)$
$⟹XB=1.8-(0.3+0.6)$
$⟹XB=0.9m$
$\therefore$ Area of quadrilateral ABCD $=$ Area of rectangle $AXYF+$ Area of triangle $CBX+$ Area of rectangle $EYCD$
$=(AX\times AF)+(\frac{1}{2}\times CX\times BX)+(EY\times ED)$
$=(FY\times AF)+(\frac{1}{2}\times 2\times 0.9)+(CD\times ED)$
$=(0.9\times 1.2)+(\frac{1}{2}\times 2\times 0.9)+(0.6\times 0.8)$
$=1.08+0.9+0.48$
$=2.46$ sq. cm

Hence, option A is correct.