Questions: Calculating the Area of a Triangle Find the area of the triangle DEF. Area = square units

Transcript text: Calculating the Area of a Triangle Find the area of the triangle DEF. \[ \text { Area }= \] $\square$ square units

Solution

Solution Steps

Step 1: Find the coordinates of the vertices.

The coordinates of the vertices are D(-8, 4), E(10, -2), and F(-8, -8).

Step 2: Calculate the base and height of the triangle.

The base of the triangle is the distance between points D and F. Since both points have the same x-coordinate, the length of the base is the difference in their y-coordinates: 4 - (-8) = 12 units.

The height of the triangle can be found by drawing a perpendicular line from E to the line segment DF. The x-coordinate of E is 10, and the x-coordinate of D and F is -8. Therefore, the height of the triangle is 10 - (-8) = 18 units.

Step 3: Calculate the area of the triangle.

The area of a triangle is given by the formula: Area = (1/2) * base * height

Substituting the values we found, we have: Area = (1/2) * 12 * 18 Area = 6 * 18 Area = 108