question_answer 1)

                The shape of a garden is rectangular in the middle and semicircular at the ends as shown in the diagram. Find the area and the perimeter of this garden. [Length of rectangle is metres].

Answer:

                Area of the garden            = Area of the rectangle           + Area of the two semicircular ends \[=\{20-(3.5+3.5)\}\,\times 7\,\,{{m}^{2}}+2\] \[\times \frac{1}{2}\pi {{\left( \frac{7}{2} \right)}^{2}}{{m}^{2}}\] \[=13\times 7\,{{m}^{2}}+\frac{49}{4}\,\pi \,{{m}^{2}}\] \[=91\,{{m}^{2}}\,+\frac{49}{4}\,\times \frac{22}{7}\,{{m}^{2}}\] \[=91\,{{m}^{2}}+\frac{77}{2}\,{{m}^{2}}\] \[=\frac{259}{2}{{m}^{2}}=129.5\,{{m}^{2}}\] Perimeter of the garden \[=2\times \{20-(3.5+3.5)\}m+2\times \pi \,\left( \frac{7}{2} \right)m\] \[=26\,m+2\times \,\frac{22}{7}\,\times \frac{7}{2}\,m\] \[=26\,m\,+22\,m=48\,m\].