This is a challenging one on several levels. My method uses equivalent ratios to make sure every condition is still true (1/4 R shaded, 1/4 S shaded, 1/6 T shaded, S:R+T=8:9) and then guess n check to see which pairs satisfy ALL the conditions. In this case, I noticed that S being 16u works so I had to find pairs for R and T such that the total is 18u. Finally, make sure the total is correct. It’s 30u, not 12u+16u+6u.

Thank you teacher!

A much faster way :

Area S : Area (R+T) = 8 : 9
This is like saying '8 units to 9 units'


Since ¼ of S is shaded,
Shaded area = 8 units ÷ 4 = 2 units


Total area of figure

= Area of S - shaded area + R + T
(so there are no overlaps)
= 8 units - 2 units + 9 units
= 15


Fraction of figure that is shaded

= 2/15

With the above method, there is no need to do any guess and check of equivalent ratios. We also realise that the info about 1/4 of R is shaded and 1/6 of T is shaded are not necessary for solving.

Thank you!

oh yea. it is much faster this way for this question. nice!

Thanks

Janice, sometimes the info can be distracting and confusing. Always be clear on what is asked of by the question

Update :


Method using those info :

Area of R : ▲△△△
Area of T : ■□□□□□

(The triangles all represent identical units for R. Same goes for squares for T.

The black coloured ones are just indicating the shaded areas and are not different units from the white ones of the same shape.)

Total of the two : 9u

But we know that ▲+ ■ = 2u

So ▲▲▲▲ + ■ ■ ■ ■ = 4 x 2u = 8u

Compare this with above :

Difference = 9u - 8u = 1u
Difference is also 2□

So 2□ = 1u
Area of T = 6□
= 2□ x 3
= 1u x 3
= 3u

Area of R = 9u - 3u = 6u

Solve accordingly.