Answer:
318.495 m²
Step-by-step explanation:
The allotment can be modelled as a rectangle with its top right corner cut off.
The width (w) and length (l) of the rectangle are:
[tex]\sf w = 18.3\; m[/tex]
[tex]\sf l = 20.4 \;m[/tex]
The base of the triangle (b) is the difference between the top and bottom edges of the allotment:
[tex]\sf b = 20.4 \;m - 7.5 \;m[/tex]
[tex]\sf b = 12.9 \;m[/tex]
The height of the triangle (h) is the difference between the left and right edges of the allotment:
[tex]\sf h = 18.3 \;m - 9.8 \;m[/tex]
[tex]\sf h = 8.5 \;m[/tex]
To find the area of the allotment, we subtract the area of the cut-off triangular corner from the area of the rectangle.
Since the area of a rectangle is the product of its width and length, and the area of a triangle is half the product of its base and height, then area of the allotment can be calculated as follows:
[tex]\begin{aligned}\textsf{Area of allotment}&= \textsf{Area of rectangle} - \textsf{Area of triangle}\\\\&= \sf (w \times l) -\left(\dfrac{1}{2}\times b\times h\right)\\\\&= \sf (18.3\; m \times 20.4\; m) - \left(\dfrac{1}{2}\times 12.9\; m\times 8.5 \;m\right)\\\\&= \sf 373.32 \;m^2 - 54.825 \;m^2\\\\&= \sf 318.495\; m^2\end{aligned}[/tex]
Therefore, the area of the allotment is 318.495 m².
