Question

What is the area of a triangle whose vertices are

Answer 1

Check the picture below.

you can pretty much count the units for the base and its height off the grid.

Answer 2

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 $R(-4,2)$ and $S(1,2)$ tell us that this line is horizontal. The y-values are constant.

Therefore $|RS|=|1--4|$

$\Rightarrow |RS|=|1+4|$

$\Rightarrow |RS|=|5|$

$\Rightarrow |RS|=5$

Also

The triangle is bounded between $y=2$ and $y=-4$.

Therefore the vertical height of interest,

$|RT|=|-4-2|$

$|RT|=|-6|$

$|RT|=6$

We can now find the area using the formula

$Area=\frac{1}{2}base\times height$

$Area=\frac{1}{2}\times6 \times 5$

$Area=3 \times 5$

$Area=15$ square units