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# I need help quick please!!

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Twelve 1 by 1 squares form a rectangle, as shown. What is the total area of the shaded region?

Jul 17, 2019

#1
+23171
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Twelve 1 by 1 squares form a rectangle, as shown. What is the total area of the shaded region?

$$\text{Let the area of the lower triangle is \dfrac{2\cdot 4}{2} = 4  }\\ \text{Let the area of the upper triangle is \dfrac{3\cdot 4}{2} = 6  }\\ \text{The area of the shaded region is 4+6=\mathbf{10}  }$$

Jul 17, 2019
edited by heureka  Jul 17, 2019
edited by heureka  Jul 17, 2019
#2
+103999
+3

Note that the shaded area is composed of two triangles...

The one on the left has a height of 4 and a base of 2.....so its area  = (1/2)(2)(4) =  4 units^2

The one on the right has a base of 3 and a height of 4....so its area  = (1/2)(3)(4)  = 6 units ^2

So.....the total shaded area  is  [ 4 + 6 ] iunits^2  = 10 units^2

Jul 17, 2019
#3
+1

Slightly different approach - let's subtract off the non-shaded region.

By Pick's Theorem, we have that the area is $$\frac{4}{2}+1 - 1 = 2.$$ Note that this only works if the vertices are lattice points and there are no crosses in the figure. Then, the area of the rectangle is $$4\times3$$, so our final answer is $$4\times3 - 2 = \boxed{10}.$$

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Jul 18, 2019