The figure is made up of 3 similar overlapping squares of side 4 cm. The squares touched one another at Corners T,U,V,W and X. Howard 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 (4 x 4)
= 48 cm
2Area of 4 triangles (due to 2 overlapping triangles)
= 4 x (
12 x 4 x 2)
= 16 cm
2 Area of the unshaded part of the figure
= 48 - 16
= 32 cm
2
(b)
Area of the shaded part
=
12 x (4 x 4)
= 8 cm
2 Total area
= 32 + 8
= 40 cm
2
Fraction of the shaded part to the figure
=
840 =
15 Answer(s): (a) 32 cm
2; (b)
15