Question:
In the rectangle shown below, PQ = 28 cm and QR = 21 cm.
The ratio of SA : AB : BQ = 3 : 2 : 5,CR is 3/4 of QC and PB = QB.
What fraction of the rectangle PQRS is shaded?
Solution:
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![P6 / Temasek / 2020 / SA2 Prelims / Paper 2 – Q12 [4 marks]](https://i0.wp.com/sgprimaths.com/wp-content/uploads/2020/09/P6_Temasek_2020_SA2_Paper2_Q12-Qns.jpg?resize=400%2C260&ssl=1)
I still do not understand why we take 4/7 of 1/2 and 2/10 of 1/2, do you mind helping me?
Hi! I would be glad to help!
Consider Triangle QRS,
Triangle QSC = 4/7 of Triangle QRS (which is 1/2 of total fig).
Therefore, Triangle QSC = 4/7 x 1/2
Consider Triangle QPS
,
Triangle PBA = 2/10 of Triangle QPS (which is 1/2 of total fig)
Therefore, Triangle PBA = 2/10 x 1/2
For both above, use the area of triangle formula (1/2 x Base x height) to consider the ratio of the area between the triangles.
When the triangles have the same height, but the base differs by the ratio, then their areas will differ by the ratio too