Question

the figure below,not drawn to scale ,is made up of two identical right angled triangles overlapping each other. find the area of the shaded part ABCD, where AD equals to 3cm.

Answer 1

We develop two equations based on the given diagram. We let x be the length from C to the point meeting the endpoint of 5. We let y be the length of CD. 

First, we determine the length from D to the endpoint of line measuring 9 cm. We use the Pythagorean theorem.
      l = sqrt ((3)² + 5²) 
      l = 5.83

Then, the equations that can be developed or established are:
    x² + 6² = y²
   9² + (5 + x)² = (y + 5.83)²

In solving for x and y, we use substitution.
From the first equation,
  y = sqrt (x² + 36)
We substitute this to the second equation y. 

The value of x is 9.51. 

y = sqrt (9.51² + 36) = 11.25.

Calculate for the area of the bigger triangle.
  A = 0.5(9 cm)(5 + 9.51 cm) = 65.295 cm²

Also calculate for the area of the smaller triangle,
  A = (0.5)(6 cm)(9.51 cm)  = 28.53 cm²

The difference between the areas is 36.765 cm².

ANSWER: 36.77 cm²