# Question

In the figure below,ABC and XYZ are identical right-angled triangles.The total area of the shaded parts is 110cm2.Find the area of the unshaded part.

How to tackle this question?

 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 = 55cm2 and U = Area ABC - Blue area = (18 x 12)/2 - 55 = 53cm2 The key is to realize that the shaded parts are equal as the same U is cut from ABC and XYZ.

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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 = 53cm2

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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

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

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