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Answer :

mhanifa

Answer:

75

Step-by-step explanation:

Refer to attachment

As the first step extending the segment BC until intersection with AD.

Since ∠A + ∠B = 90° we get right triangle by extending CB

Naming the segments a, b, c, d as pictured

The are of (ABCD) is equal to sum of areas of two right triangles:

  • Area = 1/2c(a+b) + 1/2bd

Substitute d with a-c as a = c+d, then:

  • Area = 1/2(ac+bc) + 1/2b(a-c) = 1/2(ac + bc + ab - bc) = 1/2(ab + ac)
  • Area = 1/2(ab+ac)

Applying Pythagorean to small triangle:

  • 10² = b² + (a-c)²
  • 100 = b² + a² - 2ac + c²

Applying Pythagorean to bigger triangle:

  • 20² = (a+b)² + c²
  • 400 = a² + 2ab + b² + c²

Subtracting equations we got:

  • 400 - 100 = a² + 2ab + b² + c² - (b² + a² - 2ac + c²)
  • 300 = 2ab + 2ac

This gives us the 4 times of the area which is 1/2(ab + ac), so the area is

  • 300/4 = 75
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