Question

Find the area of the polygon.

Answer 1

 Hint: Mathematics includes the study of topics which are related to quantity, structure,
space and change. To specify a figure most fundamental quantities are perimeter, area and volume. Perimeter can be defined as the total length of the boundary of a geometrical figure. Area can be defined as the space occupied by a flat shape or the surface of an object. So, using this definition we can easily solve our problem.

Complete step by step answer:
Mathematics is related to all the phenomena occurring in the world. When mathematical structures are good models of real phenomena mathematical reasoning can be used to provide insight or predictions about nature. To specify a figure most fundamental quantities are perimeter and area. Area can be defined as the space occupied by a flat shape or the surface of an object.
We first take the rectangle ABCD, the length of rectangle$=17cm$ and the width of the rectangle$=6cm$ Therefore, area of rectangle $=length\times width$
Area of rectangle$=17\times 6c{{m}^{2}}=102c{{m}^{2}}$.
Now, area of triangle$=\dfrac{1}{2}\times base\times height$
Here, base$=17cm$ and
Height$=9-6=3cm$
We calculate the height of the triangle by subtracting the width of the rectangle from the height of the polygon.
Area of triangle$=\dfrac{1}{2}\times 3\times 17=\dfrac{51}{2}c{{m}^{2}}$’
Area of triangle$=25.5c{{m}^{2}}$.
Now, Area of polygon = Area of triangle + Area of rectangle
Area of polygon$=102c{{m}^{2}}+25.5c{{m}^{2}}=127.5c{{m}^{2}}$ .
Hence, the area of the polygon is 127.5 $cm^2$.

Note: The key concept for solving this problem is the segregation of the whole area into two parts. By separating the area into rectangle and triangle be easily evaluated as the area of the whole polygon. This concept is very useful in solving complex problems.