Question

3. Find the area enclosed by each of following fig.



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Answer 1

Step-by-step explanation:

10×50=500

10×10=100

10×10=100

5×5=25

5×5=25

5×5=25

5×5=25(+)

_____

800

Answer 2

        $\text{\huge \bf \underline{Answer:}}$

        $\text{In the attachment we can see a figure with:}$

        $GH = DC = 50 \: cm$

        $HC = GD = 10 \: cm$

        $FE = AB = 20 \: cm$

        $\text{The entire length of the figure is 70}\:cm$

        $\text{It is also given that:}$

        $GDCH \text{ is a rectangle}$

        $GDE F \text{ is a trapezium}$

        $ABCH \text{ is a trapezium}$

        $\text{We have to find the area enclosed by each figure and}\\\text{we have to find the total area enclosed by the complete figure}$

        $\text{Area of rectangle} = \text{Length}\times \text{Breadth}$

$\implies \: \text{Area }GDCH = DC \times GD$

$\implies \: \boxed{\boxed{\text{Area }GDCH = 10 \times 50 = 500 \: cm^{2}}}$

        $\text{Since, }GDE F \text{ and }ABCH \text{ are congruent trapeziums}\\\text{their heights and areas are the same}$

$\implies \: \text{Area }GDE F = \text{Area }ABCH$

$\implies \: DN = HM$

         $\text{In }GDE F$

        $DN = \text{height of trapezium }GDE F$

        $DN + HM= {\text{Length of the entire figure} - GD}$

$\implies \: 2DN = {\text{Length of the entire figure} - GD}$

$\implies \: DN = \dfrac{\text{Length of the entire figure} - GD}2$

$\implies \: DN = \dfrac{70 - 50}{2}$

$\implies \: DN = \dfrac{20}{2}$

$\implies \: DN =HM = 10 \: cm$

        $\text{Area of trapezium} = \dfrac12(\text{Sum of parallel side})\times (\text{Height})$

$\implies \:\text{Area }GDE F = \dfrac12 ( GD + EF) \times (DN)$

$\implies\: \text{Area }GDE F = \dfrac12 (10 + 20) \times (10)$

$\implies\: \text{Area }GDE F = \dfrac12 (30) \times (10)$

$\implies \: \text{Area }GDE F = (30) \times (5)$

$\implies \: \boxed{\boxed{\text{Area }GDE F = \text{Area }ABCH = 150 \: cm^{2}}}$

        $\text{Area of entire figure} = \text{Area }GDCH + \text{Area }GDE F+ \text{Area }ABCH$

$\implies \: \text{Area of entire figure} = 500 + 150+ 150$

$\implies \: \boxed{\boxed{\text{Area of entire figure} = 800 \: cm^{2}}}$