Question

find the area of the given figure ​

Answer 1

$\bold{ABOUT \: FIGURE}$

The above figure have two trapezium joined at their one side and a rectangle joined to the side of second trapezium.

So, area of this figure will be

= Area of first trapezium + Area of second trapezium + Area of rectangle.

We know ,

$\huge \boxed{Area \: of \: trapezium = \dfrac{1}{2} \times (sum \: of \: parallel \: sides ) \times height}$

$\huge \boxed{Area \: of \: rectangle = length \times breadth}$

So,

$\bold{For \: 1 st \:trapezium }$

$\mathsf{Area \: of \: trapezium = \dfrac{1}{2} \times (10 + 12 ) \times 7}$

$\mathsf{Area \: of \: trapezium = \dfrac{1}{2} \times 22 \times 7}$

$\huge \boxed{\mathsf{Area \: of \: trapezium = 77 cm^{2}}}$

$\bold{For \: 2 nd \:trapezium }$

$\mathsf{Area \: of \: trapezium = \dfrac{1}{2} \times (12 + 8 ) \times 5}$

$\mathsf{Area \: of \: trapezium = \dfrac{1}{2} \times 20 \times 5}$

$\huge \boxed{\mathsf{Area \: of \: trapezium = 50 cm^{2}}}$

$\bold{For \: Area\: of \: rectangle }$

$\mathsf{Area \: of \: rectangle = length \times breadth}$

$\mathsf{Area \: of \: rectangle = 5 \times 8}$

$\huge \boxed{\mathsf{Area \: of \: rectangle = 40 cm^{2}}}$

So,

$\bold{TOTAL \: AREA = Area \: of \: first \: trapezium +}$ $\bold{Area \: of \: second \: trapezium + Area \: of \: rectangle}$

$\mathsf{TOTAL \: AREA = 77 + 50 + 40}$

$\huge \boxed{\mathsf{TOTAL \: AREA = 167 cm^{2}}}$