I have a question and I can’t find a good answer explanation anywhere. Please help!
In rectangle ABDF above (i don’t have the diagram), C and E are midpoints of sides BD and DF. What fraction of the area of the rectangle is shaded?
ETA: ACEF is shaded.
Assume the area of ABDF is 1. The area of ABC is 1/4 (can be seen by visualization, or by labelling the dimensions l,w and finding the area).
Similarly, the area of CDE is 1/8 (same as before, this triangle has same base length but 1/2 the altitude). Then the area of ACEF is 1 - 1/4 - 1/8 = 5/8.
Visualization suggested by @MITer94:
imgur dot com/liTsQ8t.jpg
Same answer, different explanation;
Let’s say the original rectangle is 4 x 2-- sides AB and DF are 4, sides AF and BD are 2. So its area is 8. (You can use any numbers, but I chose evens that are easy to split with a midpoint.)
When you draw CE, it splits two adjacent sides. So FE= ED = 2, and CD= CB = 1.
This now becomes one of the “Area of the shaded” problems you saw in geometry.
The area of triangle CDE = 1/2 (2) 1 = 1
The area of triangle ABC = 1/2 (4) 1 = 2
The area of ACEF = 8 - 1 - 2 , or 5.
It’s 5/8 of the whole picture.