question_answer 1)

                There is a pentagonal shaped park as 'shown in the figure. For finding its area Jyoti and Kavita divided it in two different ways.                                                       Find the area of this park using both ways. Can you suggest some other way of finding its area?

Answer:

                Jyoti?s diagram Area of the park \[=2\times \,\left[ \frac{(15+30)}{2}\times \frac{15}{2} \right]\] \[=\frac{675}{2}\] \[=337.5\,{{m}^{2}}\] Kavita's diagram Area of the park                 \[=15\times 15\,{{m}^{2}}\,+\frac{15\times (30-15)}{2}\,{{m}^{2}}\] \[=225\,{{m}^{2}}+\frac{225}{2}{{m}^{2}}\] \[=225\,{{m}^{2}}+\,112.5\,{{m}^{2}}\] \[=337.5\,{{m}^{2}}\] Another way of finding the area   Area of the park \[=\frac{15\times (30-15)}{2}\,{{m}^{2}}+2\times \left[ \frac{15\times 15}{2} \right]\,{{m}^{2}}\] \[=\,337.\,5\,{{m}^{2}}\].