Question

Answer for the following!​

Answer 1

$\large\underline{\sf{Solution-}}$

Case :- 1 Jyoti Diagram

Jyoti divide the pentagon in to two trapezium of equal areas, whose parallel sides are 15 cm and 30 cm respectively and distance between parallel lines is 15/2 cm

We know,

Area of trapezium whose length of parallel sides are a units and b units respectively and distance between parallel lines is h units, is

$\color{green}\boxed{ \rm{ \: \: Area_{(trapezium)} \: = \: \frac{1}{2} \times (a + b) \times h \: \: \: }}$

So,

$\rm \: Area_{(pentagon)}$

$\rm \: = \: 2 \times Area_{(trapezium)}$

$\rm \: = \: 2 \times \dfrac{1}{2} \times (30 + 15) \times \dfrac{15}{2}$

$\rm \: = \: 45 \times \dfrac{15}{2}$

$\rm \: = \: \dfrac{675}{2} \: {cm}^{2}$

$\color{green}\rm\implies \boxed{ \rm{ \:\:Area_{(pentagon)} \: = \: \frac{675}{2} \: {cm}^{2} \: \: }}$

Case :- 2 Rashida Diagram

Rashida divides the pentagon in to two figures namely square of side 15 cm and triangle having base 15 cm and height 15 cm.

$\rm \: Area_{(pentagon)}$

$\rm \: = \: Area_{(square)} + Area_{(triangle)}$

$\rm \: = \: {15}^{2} + \frac{1}{2} \times 15 \times 15$

$\rm \: = \: 225 + \frac{225}{2}$

$\rm \: = \: \frac{450 + 225}{2}$

$\rm \: = \: \frac{675}{2} \: {cm}^{2}$

Hence,

$\color{blue}\rm\implies \boxed{ \rm{ \:\:Area_{(pentagon)} \: = \: \frac{675}{2} \: {cm}^{2} \: \: }}$

From this, we concluded that area remains the same.

$\rule{190pt}{2pt}$

Additional Information :-

$\begin{gathered}\begin{gathered}\boxed{\begin {array}{cc}\\ \dag\quad \Large\underline{\bf Formulas\:of\:Areas:-}\\ \\ \star\sf Square=(side)^2\\ \\ \star\sf Rectangle=Length\times Breadth \\\\ \star\sf Triangle=\dfrac{1}{2}\times Base\times Height \\\\ \star \sf Scalene\triangle=\sqrt {s (s-a)(s-b)(s-c)}\\ \\ \star \sf Rhombus =\dfrac {1}{2}\times d_1\times d_2 \\\\ \star\sf Rhombus =\:\dfrac {1}{2}d\sqrt {4a^2-d^2}\\ \\ \star\sf Parallelogram =Base\times Height\\\\ \star\sf Trapezium =\dfrac {1}{2}(a+b)\times Height \\ \\ \star\sf Equilateral\:Triangle=\dfrac {\sqrt{3}}{4}(side)^2\end {array}}\end{gathered}\end{gathered}$

Answer 2

Answer:

I hope this helps you and thank you