Quadrilateral

Radit2125 said:
Yes, I am familiar with it. I made a mistake. In the space we should write a+ b+ c+ d
Click to expand...
Great, can you complete this?
Quadrilateral area = area of 4 shaded triangles + 4 other triangles + 4 diff triangles + 4 more triangles = 4 ( ... )
Parallelogram area = area of 2 shaded triangles + 2 other triangles + 2 diff triangles + 2 more triangles = 2 ( ... )
 
There are 4 types of small triangles. Make their areas a, b, c, d.
Quadrilateral area = 4a ...
Parallelogram area = 2a ...
Please complete. Then use the distributive property. Then write the expression for the ratio of 2 areas. Then simplify. You should get 1/2.
 
Quadrilateral area = 4a + 4b+4c+4d
Parallelogram area = 2a +2b+2c+2d
So, the ration of the 2 area, Parallelogram area to Quadrilateral area= (2a +2b+2c+2d) / (4a + 4b+4c+4d)= 2(a+b+c+d)/4(a+b+c+d)= 2/4=1/2
 
lev888 said:
There are 4 types of small triangles. Make their areas a, b, c, d.
Quadrilateral area = 4a ...
Parallelogram area = 2a ...
Please complete. Then use the distributive property. Then write the expression for the ratio of 2 areas. Then simplify. You should get 1/2.
Click to expand...
Thank You for the help
 
Radit2125 said:
Quadrilateral area = 4a + 4b+4c+4d
Parallelogram area = 2a +2b+2c+2d
So, the ration of the 2 area, Parallelogram area to Quadrilateral area= (2a +2b+2c+2d) / (4a + 4b+4c+4d)= 2(a+b+c+d)/4(a+b+c+d)= 2/4=1/2
Click to expand...
Yes. Can you prove that the triangles in each of the 4 sets are congruent?
 
Radit2125 said:
I would like only to ask if I should connect the four midpoints
Click to expand...
To form the second quadrilateral? Yes. You should include in the diagram whatever you need to justify each step in your solution.
 
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