Question

Find the area of the following polygons:

Answer 1

Hint:- We had to only find the areas of all the triangles and rectangle in a polygon. And then the area of the polygon will be the sum of areas of all shapes inside it.
Let us first do the naming of the given polynomial. So, it becomes easy to find the area of triangle and rectangle.

Complete step-by-step answer:

As we know that the above figure is symmetric.
So, the side AE is equal to BD and AF = FE = BC = CD.
So, we can find the area of any one triangle and that will also be equal to the area of all the other triangles AFH, FHE, BCG and CDG
So, let us find the area of triangle AFH.
As we know that area of right-angled triangle is equal to \[\dfrac{1}{2} \times {\text{Base}} \times {\text{Height}}\]
So, the area of triangle AFH = \[\dfrac{1}{2} \times {\text{FH}} \times {\text{AH}} = \dfrac{1}{2} \times 10 \times \dfrac{{35}}{2} = \dfrac{{350}}{4} = 87.5c{m^2}\]
Now the area of triangle AFH = FHE = BCG = CDG = \[87.5c{m^2}\]
Now let us find the area of the rectangle ABDE.
So, as we know that the formula for area of rectangle is = \[{\text{Length}} \times {\text{Breadth}}\]
So, the area of rectangle ABDE = \[{\text{AE}} \times {\text{AB}} = 35 \times 12 = 420c{m^2}\]
Now as we can see in the given figure that the area of polygon = Area of triangle AFH + Area of triangle FHE + Area of triangle BCG + Area of triangle CDG + Area of rectangle ABDE = \[87.5 + 87.5 + 87.5 + 87.5 + 420 = 770c{m^2}\]
Hence, the area of the given polygon will be equal to \[770c{m^2}\].

Note:- Whenever we come up with this type of problem then first, we have to divide the given polygon into small squares, rectangles and triangles because we know the formula to find the area of rectangle, square and triangle and their side lengths is also given. After that we can find the area of all small parts and then add them to find the area of the polygon. This will be the easiest and efficient way to find the solution of the problem.