Given:
The diagram of a figure with sides 14 ft, 30 ft, 21 ft and 18 ft.
To find:
The area of the figure.
Solution:
From the given figure it is clear that if we cut a corner of a rectangle, then we get the same figure.
The sides of a the rectangle are 30 ft and 21 ft.
The height of the triangular part is (30 ft - 18 ft) and the base is (21 ft - 14 ft).
So, the height of the triangular part is 12 ft and the base is 7 ft.
The area of the rectangle is:
[tex]A_1=length\times width[/tex]
[tex]A_1=30\times 21[/tex]
[tex]A_1=630[/tex]
The area of the triangular part is:
[tex]A_2=\dfrac{1}{2}\times base \times height[/tex]
[tex]A_2=\dfrac{1}{2}\times 12 \times 7[/tex]
[tex]A_2=6 \times 7[/tex]
[tex]A_2=42[/tex]
Now, the area of the given figure is:
[tex]A=A_1-A_2[/tex]
[tex]A=630-42[/tex]
[tex]A=588[/tex]
Therefore, the area of the given figure is 588 sq. ft.
