The figure is made up of 3 similar overlapping squares of side 12 m. The squares touched one another at Corners F,G,H,J and K. Riordan shaded the parts where the squares overlapped each other.
- Find the area of the unshaded part of the figure.
- What fraction of the figure is the shaded part?
(a)
Area of 3 squares
= 3 x (12 x 12)
= 432 m
2Area of 4 triangles (due to 2 overlapping triangles)
= 4 x (
12 x 12 x 6)
= 144 m
2 Area of the unshaded part of the figure
= 432 - 144
= 288 m
2
(b)
Area of the shaded part
=
12 x (12 x 12)
= 72 m
2 Total area
= 288 + 72
= 360 m
2
Fraction of the shaded part to the figure
=
72360 =
15 Answer(s): (a) 288 m
2; (b)
15