Answer :
To determine the area of the plot, we need to understand its shape. Based on the givens: two sides measure 32 metres and 24 metres with a perfect right angle between them, and the other two sides are both 25 metres long, the plot forms a quadrilateral known as a 'kite'.
In a kite-shaped plot where a right angle is present, we can split it into two right-angled triangles.
Identify the Right Triangle:
- The sides 32 metres and 24 metres form the two legs of a right triangle.
Calculate the Area of the Right Triangle:
- The formula for the area of a right triangle is [tex]\frac{1}{2} \times \text{base} \times \text{height}[/tex].
- Here, the base is 32 metres and the height is 24 metres.
[tex]\text{Area of the right triangle} = \frac{1}{2} \times 32 \times 24 = \frac{1}{2} \times 768 = 384\, \text{square metres}[/tex]
Area of the Kite-shaped Plot:
- Since the plot consists of two identical triangles (as both other sides of the kite are 25 metres each), the total area is double that of one triangle.
[tex]\text{Total Area} = 2 \times 384 = 768\, \text{square metres}[/tex]
In conclusion, the area of the plot is 768 square metres.
