What is the area of a triangle whose vertices are R(−4, 2),S(1, 2), and T(−5, −4)? Enter your answer in the box

ANSWER

15 square units.

EXPLANATION

This triangle has one of its height(altitudes) falling outside the triangle.

We determine the base using absolute value method. This is because the coordinates of [tex]R(-4,2)[/tex] and [tex]S(1,2)[/tex] tell us that this line is horizontal. The y-values are constant.

Therefore [tex]|RS|=|1--4|[/tex]

[tex]\Rightarrow |RS|=|1+4|[/tex]

[tex]\Rightarrow |RS|=|5|[/tex]

[tex]\Rightarrow |RS|=5[/tex]

Also

The triangle is bounded between [tex]y=2[/tex] and [tex]y=-4[/tex].

Therefore the vertical height of interest,

[tex]|RT|=|-4-2|[/tex]

[tex]|RT|=|-6|[/tex]

[tex]|RT|=6[/tex]

We can now find the area using the formula

[tex]Area=\frac{1}{2}base\times height[/tex]

[tex]Area=\frac{1}{2}\times6 \times 5[/tex]

[tex]Area=3 \times 5[/tex]

[tex]Area=15[/tex] square units