The area of the given figure is 552 m^2 which is option (d).
- The area of a parallelogram is the area enclosed by the parallelogram in a particular two-dimensional space. Assuming "a" and "b" are a set of parallel sides of a parallelogram and h is the height, the formula for its area based on the length and height of the sides is given by Area = Base area x Height .......(1)
- The area of a triangle is defined as the total area bounded by her three sides of a particular triangle. It's basically equal to half the base multiplied by the height, so [tex]A=\frac{1}{2} \times b\times h[/tex]. ...(2) .
We have given a figure of FGHIE .
From the figure , we can see that FHIE is a parallelogram with a base 23m and height = 18 m
Put h = 18 m , b = 23 m in equation (1) , we get
[tex]A=23\times18\\A=414m^2[/tex]
From the figure , we can see that GHI is a triangle with a base 23 m and height 12 m
Put b = 23 m and h = 12 m in equation (2) , we get
[tex]A=\frac{1}{2} \times23\times12\\\\A=\frac{276}{2} \\\\A=138m^2[/tex]
Total area of FGHIE = area of parallelogram FGIE + area of triangle GHI
[tex]=141+138\\=552m^2[/tex]
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