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Triangle KLM, with vertices K(2,5), L(6,3), and M(9,9), is drawn inside a rectangle.

What is the area, in square units, of triangle KLM?

Answer :

The area of the triangle is given as Area = 15.56 square units

What is a triangle?

Recall that a triangle is a three-sided polygon that consists of three edges and three vertices

We shall first find the sides of the triangle as follows

The distance KL = [tex]\sqrt{(3-5)^{2} + (6-2)^{2} }[/tex]

KL = [tex]\sqrt{(-2)x^{2} ^{2} + (4)^{2} }[/tex]

KL = [tex]\sqrt{4+16} = \sqrt{20}[/tex]

KL = 4.5

The distance KM = [tex]\sqrt{(5-9)^{2} + (2-9)x^{2} ^{2} } \\KM = \sqrt{(-7)^{2} + (-4)^{2} }[/tex]

KM = [tex]\sqrt{49+16} = \sqrt{65} = 8.1[/tex]

The distance LM = [tex]\sqrt{(3-9)^{2} + (6-9)^{2} } \\LM = \sqrt{-6^{2} + -3^{2} } \\LM = \sqrt{36+9 = \sqrt{45} } \\= 6.7[/tex]

Having determined all the three sides of the triangle, Let us use Hero's formula to determine the area of the triangle by

Area = [tex]\sqrt{s[(s-a)(s-b)(s-c)} \\[/tex]

where s = (a+b+c)/2

s= (4.5+8.1+6.7)/2

s= 19.32

s= 9.7

Applying the formula we have

Area = [tex]\sqrt{9.7[(9.7-4.5)(9.7-8.1)(9.7-6.7)}[/tex]

Area = [tex]\sqrt{9.7[(5.2)(1.6)(3)}[/tex]

Area = √242.112

Therefore the Area = 15.56 square units

Learn more about area of triangles on https://brainly.com/question/19305981

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