Question

Which is the area of triangle LMN? Group of answer choices 24 square units 27 square units 54 square units 48 square units

Answer 1

√65/2 square units

Explanation:

Find the diagram attached

Area of the triangle = 1/2 * base * height

To get the base and height, we will use the distance formula;

Area of the triangle LMN = 1/2 * LM * MN

For MN

Given the coordinate M(3, 2) and N(1, 3)

MN = √(3-2)²+(1-3)²

MN = √1²+(-2)²

MN = √1+4

MN = √5

For LM;

Given the coordinate L(1, -1) and M(3, 2)

LM = √(2-(-1))²+(3-1)²

LM = √(2+1)²+(2)²

LM = √3²+(2)²

LM = √9+4

LM = √13

Area of the triangle LMN = 1/2 * √13 * √5

Area of the triangle LMN = √65/2 square units