There is a missing shaded area. You should shade the semicircle inside the rectangle

Shaded area of △ : unshaded area of △ : total area of △ = 3 : 4 : 7

Since the shaded quarter circle is ¼ of a full circle, and the full circle's area is 360cm² ,

Area of shaded quarter circle
= 360cm² ÷ 4 = 90cm²

Now area of shades quarter circle is also 3 units since it's the shaded area of the △.

3 units = 90cm²
1 unit = 90cm² ÷ 3 = 30cm²

Since area of △ is 7 units,
Area of △ = 30cm² x 7 = 210cm²

Understood, thx

Typing b now.

Area of △ : area of rectangle
= 2 : 3

So area of rectangle = △ area ÷ 2 x 3

= 210cm² ÷ 2 x 3
= 105cm² x 3
= 315cm²

The semicircle is ½ of the full circle.
So its area = 360cm² ÷ 2 = 180cm²

Total shaded area = 180cm² + 90cm²
= 270cm²

Unshaded area of rectangle
= Total area of rectangle - area of that shaded semicircle
= 315cm² - 180cm²
= 135cm²

Unshaded area of △ = 4 units
= 4 x 30cm²
= 120cm²

Unshaded area of circle
= Area of whole circle - total shaded area
(Since it's all within the circle)

= 360cm² - 270cm²
= 90cm²

Total unshaded area
= 90cm² + 120cm² + 135cm²
= 345cm²

Ratio of total shaded to total unshaded area

= 270 : 345
= 90 : 115 (divided by 3)
= 18 : 23 (divided by 5)

Or simply key into calculator 270/345 to find the simplest fraction

Alternative working :

Since ratio of triangle to rectangle
= 2 : 3

△ shaded area : △unshaded area : △total
area = 3 : 4 : 7

Change the units in the ratio and the units for area of triangle to be the same since they are giving the same area.

Common multiple of 7 and 2 is 7 x 2 = 14. So change both to 14.


2 : 3 = 14 : 21 (multiply by 7)

3 : 4 : 7 = 6 : 8 : 14 (multiply by 2)


From this we see that :

Rectangle area = 21 units,
Triangle area = 14 units

Shaded quarter circle = 6 units

Then shaded semicircle = 6 units x 2
= 12 units

Total shaded area = 6 + 12 = 18 units

Since one semicircle and one quarter circle are shaded, this means in total ¾ of circle is shaded.

So unshaded portion or circle
= 1 - ¾ = ¼ of circle, which is just 6 units since it has same area as that shaded quarter circle.


Total area of figure
= Rectangle + triangle + unshaded part of circle

= 21 units + 14 units + 6 units
= 41 units

Unshaded area = total - shaded area
= 41 units - 18 units
= 23 units



Shaded : unshaded

= 18 : 23