Question

The corners of a triangle garden are marked with trees at coordinates (0,3),(3,0), and (4,3). Let a denote the area of the garden, in square units. Which of the following is true?

Answer 1

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=(1)/(2)|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|`

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=(1)/(2)|0(0-3)+3(3-3)+4(3-0)|`

`a=(1)/(2)|0(-3)+3(0)+4(3)|`

`a=(1)/(2)|0+0+12|`

`a=(1)/(2)* 12`

`a=6`

Therefore, the area of the garden is a=6 square units.