Question

Find area of the green track whose width is 2 m, if in rectangles PQRS and ABDC, AB = 6 m and BD=SR=PQ = 8 m. (use $\pi =3.14$)

• A. 13.26 $m^2$
• B. 39.78 $m^2$
• C. 76.28 $m^2$
• D. 97.24 $m^2$

Answer 1

The correct option is D 97.24 $m^2$

Area of green track
= Area of circle having diameter PS or QR - area of circle having diameter AB or CD + Area of rectangle PQRS -
Area of rectangle ABDC

Area of circle having diameter AB or CD
= $\pi$$r^2$
= $\pi$$\times$$3^2$ ...(radius = $\frac{diameter}{2}$= $\frac{6}{2}$ = 3 m)
= 3.14$\times$9 = 13.26 $m^2$

PS=QR= PA+AB + BS = 2 + 6 + 2 = 10
Area of circle having diameter PS or QR
= $\pi$$r^2$
= $\pi$$\times$$5^2$ ...(radius = $\frac{diameter}{2}$ = $\frac{10}{2}$ = 5)
= 3.14$\times$25 = 78.5 $m^2$

Area of rectangle = length$\times$bradth
Area of rectangle PQRS = PS$\times$SR
= 10$\times$8 = 80 $m^2$
Area of rectangle ABDC= AB$\times$BD
= 6$\times$8 = 48 $m^2$
Area of green track
= 78.5 - 13.26 + 80 - 48 = 97.24 $m^2$