Pls help to solve, thanks

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# Question

# Answer

The answer key is wrong because it has double-counted for the overlapping parts as seen in my diagram above. The figure is made up of the 3 shapes overlapping at the shaded areas so it should be 27u instead of 33u.. hence my solution as follows still holds:

Square Triangle Rectangle Total

5u 8u 20u 33u

1/5 x 20u = 4u = right shaded part of triangle

Total shaded part of triangle = 3/4 x 8u = 6u => Unshaded part = 8u-6u = 2u

Hence total figure taking away the overlapping parts = 33u – 6u = 27u or 5u+2u+20u = 27u

Fraction of shaded part of the figure = Shaded overlapping parts/ total figure

= 6u/27u = 2/9

The answer key is wrong because it has double-counted for the overlapping parts as seen in my diagram above. The figure is made up of the 3 shapes overlapping at the shaded areas so it should be 27u instead of 33u.. hence my solution as follows still holds:

Square Triangle Rectangle Total

5u 8u 20u 33u

1/5 x 20u = 4u = right shaded part of triangle

Total shaded part of triangle = 3/4 x 8u = 6u => Unshaded part = 8u-6u = 2u

Hence total figure taking away the overlapping parts = 33u – 6u = 27u or 5u+2u+20u = 27u

Fraction of shaded part of the figure = Shaded overlapping parts/ total figure

= 6u/27u = 2/9

Understood. Thank you !

Is the answer key 2/9?

No, the answer key is 6/33

The answer key is wrong because it has double-counted for the overlapping parts as seen in my diagram above. The figure is made up of the 3 shapes overlapping at the shaded areas so it should be 27u instead of 33u.. hence my solution as follows still holds:

Square Triangle Rectangle Total

5u 8u 20u 33u

1/5 x 20u = 4u = right shaded part of triangle

Total shaded part of triangle = 3/4 x 8u = 6u => Unshaded part = 8u-6u = 2u

Hence total figure taking away the overlapping parts = 33u – 6u = 27u or 5u+2u+20u = 27u

Fraction of shaded part of the figure = Shaded overlapping parts/ total figure

= 6u/27u = 2/9

Square Triangle Rectangle Total

5u 8u 20u 33u

1/5 x 20u = 4u = right shaded part of triangle

Total shaded part of triangle = 3/4 x 8u = 6u => Unshaded part = 8u-6u = 2u

Hence total figure taking away the overlapping parts = 33u – 6u = 27u or 5u+2u+20u = 27u

Fraction of shaded part of the figure = Shaded overlapping parts/ total figure

= 6u/27u = 2/9

Understood. Thank you !

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