question_answer

The shape of a garden is rectangular in the middle and semicircular at the ends as shown in the diagram. Find the area and perimeter of this garden. [Length of rectangle is \[20-\left( 3.5\text{ }+\text{ }3.5 \right)\]meters]

Answer:

Length of rectangle \[=20-\left( 3.5+3.5 \right)\]

\[=20-7=13m\]

Breadth of rectangle = 7 m

The area of rectangular \[=l\times b=13\times 7=91\,{{m}^{2}}\]

The perimeter of rectangular part \[=2\left( \text{l}\,\text{+}b \right)\]

\[=2\left( 13+7 \right)=40m~\]

Now,       radius of each semicircle = 3.5 m

The area of both semicircular part \[=\pi {{r}^{2}}\]

=\[=\frac{22}{7}\times 3.5\times 3.5\]

= 38.5m2

The perimeter of both semicircular \[=2\pi r\]

\[=2\times \frac{22}{7}\times 3.5=22m\]

\[\therefore \]The area of whole garden=The area of rectangular part

+ The area of semi-circular part

\[=91{{m}^{2}}+38.5{{m}^{2}}\]

\[=\text{ }129.5{{m}^{2~}}\]

The perimeter of whole garden = The perimeter of rectangular part

+ The perimeter of semi-circular part

= 40 m + 22 m

= 62 m.