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.
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Question
Answer
mr.tan
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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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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 = 53cm2
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
Crucial point is to take note that the shaded part + 2 unshaded part = area of ABC+ area of XYZ