316 cm²
A polygon is given to us and we are interested in finding out the area of the polygon .
- Here we can see that the polygon is made up of a rectangle and a triangle .
We can separately find out their areas and then add them up to find out the area of the polygon.
So that ,
[tex]\sf\longrightarrow Area = ar(\triangle)+ ar(\blacksquare) \\[/tex]
- We know that the area of rectangle is length × breadth and that of triangle is 1/2 × base × height . So ,
[tex]\sf\longrightarrow Area = \dfrac{1}{2}(base)(height) + (length)(breadth) \\[/tex]
- Here height of triangle can be calculated by subtracting the lengths 18cm and 14cm and its base can be calculated by subtracting CD from BD ( see figure in attachment.)
[tex]\sf\longrightarrow Area = \dfrac{1}{2}(4cm)(11cm)+(21cm)(14cm)\\[/tex]
[tex]\sf\longrightarrow Area = 22cm^2 + 294cm^2\\[/tex]
[tex]\sf\longrightarrow \underline{\boxed{\bf Area_{(polygon)}= 316cm^2}} \\[/tex]
