Question

Find the area of the shaded region in the figure above using two different ways. Do you get the same

answer both ways? Investigate what's going on here.

Answer 1

Below

Explanation:

First way:

Find the area of the big triangle and subtract the area of the rectangle.

Area of shaded part = 1/2 * 25 * 34 - 10*24 = 185 m^2

Second way:

Add the area of the 3 shaded triangles:

= 1/2 * 15 * 24 + 1/2 * 5 * 10 + 1/2 * 5 * 10

= 180 + 25 + 25 = 230 m^2

The areas are different. The reason must be that given lengths are not possible for this diagram.

Check The length of the hypotenuse of the large triangle by 2 different methods:

The hypotenuse = √(25^2 + 17^2)

= 30.23.

Now let's work out the hypotenuse of the shaded triangles:

Top one = √(15^2 ^ 12^2) = 19.21

Bottom one = √((5^2 + 10^2) = 11.18

Adding these we get 30.39 which is different than previously calculated but it should be the same.

So what we have here is impossible geometry. This accounts for the different areas.