Question

A challenge to all math experts...

Answer 1

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