Find Area of Triangle QLP & XYZ in Hexagon

AI Thread Summary
To find the area of triangles QLP and XYZ within a hexagon formed by three squares attached to the sides of a right-angled triangle, the area can be calculated using the formula A = 1/2 * ab * sin C. The total area of the figure includes the areas of the two squares and the two triangles, which can be rearranged to form a rectangle. The areas of the squares are calculated as a² and b², while the triangles contribute 2 * (1/2 * a * b). The problem is resolved by summing these areas, confirming the approach is effective.
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Homework Statement



A right angled triangle has 3 squares attached to each side(the measure of each is givn in the figure). a hexagon is thus formed. Find its area.

Homework Equations



none

The Attempt at a Solution


I have found the area of the figure except for the following triangles.
triangle QLP and triangle XYZ
Please help me with these two triangles!
 
Last edited:
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The figure is here

The figure is here
 

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It may help to know that you can find the area of a triangle to be:

A = \frac{1}{2}ab\sin C
 
Last edited:
You want the sum of the areas of four regions:

Two are squares, and two are triangles which together can be repositioned to form a rectangle. a*a, b*b, and two of a*b.
 
Thanks, the problem seems solved. Thanks a lot!
 

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