Question

What is the area of the triangle whose vertices are D(−7, 3) , E(−7, 9) , and F(−11, 7) ? Enter your answer in the box.

Answer 1

ANSWER

The area of triangle DEF is $12$ square units.

EXPLANATION

The area of triangle DEF can be found using the formula,

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

From the diagram, we can see that the height of the triangle is bounded between $x=-7$ and $x=-11$.

We use the absolute value method to find the height to be,

$Height=|-7--11|=|-7+11|=|4|=4$.

The base of the triangle is |DE|.

We can again use the absolute value method to to determine the length of the base to be,

$Length=|9-3|=|6|=6$

We now calculate the area to obtain,

$Area=\frac{1}{2}\times 6\times 4 =3\times 12=12$

Therefore the area of the triangle 12 square units