Question

Given:

Answer 1

Answer:

84 square units.

Step-by-step explanation:

If LM - KN = 4, then denote KN = x and LM = x+4.

1. Consider right triangle KLM. By the Pythagorean theorem,

$KL^2 =ML^2+MK^2,\\ \\15^2=(x+4)^2+MK^2.$

2. Consider right triangle KMN. By the Pythagorean theorem,

$MN^2 =NK^2+MK^2,\\ \\13^2=x^2+MK^2.$

Subtract these two equations:

$15^2-13^2=(x+4)^2-x^2,\\ \\225-169=x^2+8x+16-x^2,\\ \\56=8x+16,\\ \\8x=56-16,\\ \\8x=40,\\ \\x=5\ un.$

Then

$13^2=5^2+MK^2,\\ \\MK^2=169-25,\\ \\MK^2=144,\\ \\MK=12\ un.$

The area of KLMN is

$A_{KLMN}=\dfrac{LM+KN}{2}\cdot MK=\dfrac{5+9}{2}\cdot 12=14\cdot 6=84\ un^2.$