Question

what is the area of triangle lmn? 12 square units 14 square units 15 square units 24 square units

Explanation:

Step1: Identify coordinates of points

From the graph, we can see the coordinates:

• \( L(-1, 2) \)
• \( M(-1, -4) \)
• \( N(4, -4) \)

Step2: Find the base length

The base \( MN \) is horizontal (since \( y \)-coordinates of \( M \) and \( N \) are the same). The length of \( MN \) is the difference in \( x \)-coordinates:
\( \text{Length of } MN = |4 - (-1)| = |4 + 1| = 5 \) units.

Step3: Find the height

The height is the vertical distance from \( L \) to \( MN \). Since \( MN \) is horizontal at \( y = -4 \), the vertical distance from \( L(-1, 2) \) to \( y = -4 \) is:
\( \text{Height} = |2 - (-4)| = |2 + 4| = 6 \) units.

Step4: Calculate the area of the triangle

The formula for the area of a triangle is \( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \).
Substituting the values:
\( \text{Area} = \frac{1}{2} \times 5 \times 6 \)
\( \text{Area} = \frac{1}{2} \times 30 = 15 \) square units.

Answer:

15 square units