In the figure below,ABC and XYZ are identical right-angled triangles.The total area of the shaded parts is 110cm^{2.Find the area of the unshaded part.}

How to tackle this question?

In the figure below,ABC and XYZ are identical right-angled triangles.The total area of the shaded parts is 110cm^{2.Find the area of the unshaded part.}

How to tackle this question?

mr.tan

Let U be Unshaded area. Blue area = Area ABC - U Green area = Area XYZ - U But Area ABC = Area XYZ So Blue area = Green area Thus Blue area = 110/2 = 55cm |

sushi88

The 2 identical triangles when stacked together has 2 times of the unshaded part.

Area of both identical triangles = 2 x (1/2) x 12 x 18 = 216

Area of 2 times of unshaded part(since stacked together) = 216 -110 = 106

Hence area of unshaded part = 106/2 = 53cm^{2}

waterflow

*If ABC and XYZ are identical triangle, then length XY = length CB = 18cm*

*And length AC = length ZY = 12cm*

*Area of triangle ABC = Area of triangle XYZ = 18*12/2= 108 cm square*

*2 * unshaded part + shaded part = 2*108*

*2 * unshaded part = 2*108-110 = 106*

*Unshaded part = 53 cm square*

*Cru*cial point is to take note that the shaded part + 2 unshaded part = area of ABC+ area of XYZ