Area - Aptitude MCQ Questions and Solutions with Explanations

Answer: Option D

Let the length of each side of the square be x cm
Then, length of rectangle = (x + 5) cm and its breadth = (x - 3) cm
$$\eqalign{ & \therefore \left( {x + 5} \right)\left( {x - 3} \right) = {x^2} \cr & \Rightarrow {x^2} + 2x - 15 = {x^2} \cr & \Rightarrow x = \frac{{15}}{2} \cr} $$
∴ Length :
$$\eqalign{ & = \left( {\frac{{15}}{2} + 5} \right)cm \cr & = \frac{{25}}{2}cm \cr} $$
Breadth :
$$\eqalign{ & = \left( {\frac{{15}}{2} - 3} \right)cm \cr & = \frac{9}{2}cm \cr} $$
Hence, perimeter :
$$\eqalign{ & = 2\left( {l + b} \right) \cr & = 2\left( {\frac{{25}}{2} + \frac{9}{2}} \right)cm \cr & = 34\,cm \cr} $$

Answer: Option B

$$\eqalign{ & AD = \sqrt {{4^2} + {6^2}} cm \cr & \,\,\,\,\,\,\,\,\,\,\, = \sqrt {52} \,cm \cr & \,\,\,\,\,\,\,\,\,\,\, = 2\sqrt {13} \,cm \cr & \,\,\,\,\,\,\,\,\,\,\, = \left( {2 \times 3.6} \right)cm \cr & \,\,\,\,\,\,\,\,\,\,\, = 7.2\,cm \cr} $$

Area of the whole figure :
$$ = {\text{Area (}}\vartriangle {\text{AED) + }}$$   $${\text{ Area (}}\square {\text{ ABCD) + }}$$   $${\text{Area (}}\vartriangle {\text{BFC)}}$$
$$ = \left[ {\left( {\frac{1}{2} \times 4 \times 6} \right) + \left( {12 \times 7.2} \right) + \left( {\frac{1}{2} \times 4 \times 6} \right)} \right]c{m^2}$$
$$\eqalign{ & = \left( {24 + 86.4} \right)c{m^2} \cr & = 110.4\,c{m^2} \cr} $$