Given:
Three corner points of a triangular garden are (0,3),(3,0), and (4,3).
To find:
The area of the garden.
Solution:
We know that, area of a triangle is
![A=\dfrac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|](https://tex.z-dn.net/?f=A%3D%5Cdfrac%7B1%7D%7B2%7D%7Cx_1%28y_2-y_3%29%2Bx_2%28y_3-y_1%29%2Bx_3%28y_1-y_2%29%7C)
Let a denote the area of the garden, in square units.
Three vertices of the triangular garden are (0,3),(3,0), and (4,3). So, area of the triangular garden is
![a=\dfrac{1}{2}|0(0-3)+3(3-3)+4(3-0)|](https://tex.z-dn.net/?f=a%3D%5Cdfrac%7B1%7D%7B2%7D%7C0%280-3%29%2B3%283-3%29%2B4%283-0%29%7C)
![a=\dfrac{1}{2}|0(-3)+3(0)+4(3)|](https://tex.z-dn.net/?f=a%3D%5Cdfrac%7B1%7D%7B2%7D%7C0%28-3%29%2B3%280%29%2B4%283%29%7C)
![a=\dfrac{1}{2}|0+0+12|](https://tex.z-dn.net/?f=a%3D%5Cdfrac%7B1%7D%7B2%7D%7C0%2B0%2B12%7C)
![a=\dfrac{1}{2}\times 12](https://tex.z-dn.net/?f=a%3D%5Cdfrac%7B1%7D%7B2%7D%5Ctimes%2012)
![a=6](https://tex.z-dn.net/?f=a%3D6)
Therefore, the area of the garden is a=6 square units.