Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
Semi-circular lawns are attached to the edges of a rectangular field measuring 42 m × 35 m. The area of the total field is
(a)$1358 \mathrm{m}^{2}$
(b)$3818.5 \mathrm{m}^{2}$
(c)$5813 \mathrm{m}^{2}$
(d)$8318 \mathrm{m}^{2}$
Answer
Answer (as printed): B
Explanation
Clearly, the radii of the semi-circular ends along the length and breadth are $\left(\frac{42}{2}\right) \mathrm{m}$ and $\left(\frac{35}{2}\right) \mathrm{m}$. i.e. 21 m and 17.5 m respectively. ∴ Area of the total field = Area of rectangle with dimensions 42 m × 35 m + 2 × Area of semi-circle with radius 21 m + 2 × Area of semi-circle with radius 17.5 m $$\begin{aligned} & =\left(42 \times 35+2 \times \frac{22}{7} \times \frac{21 \times 21}{2}+2 \times \frac{22}{7} \times \frac{17.5 \times 17.5}{2}\right) \mathrm{m}^{2} \\ & =(1470+1386+962.5) \mathrm{m}^{2}=3818.5 \mathrm{m}^{2} . \end{aligned}$$