4a) 110 square centimetres
4b) 127 square centimetres
6) 292 square centimetres
8) 800 tiles
Step-by-step explanation:
4. We need to find the area of the large rectangle and then deduct the area of the unshaded part:
a) The large rectangle has dimensions 12 cm by 15 cm. Its area is:
A = 12 * 15 = 180 square centimetres
The unshaded part has a length of 15 - (3 + 2) cm i.e. 10 cm and a width of 7 cm. Its area is:
a = 10 * 7 = 70 square centimetres
Therefore, the area of the shaded part is:
A - a = 180 Â - 70 = 110 square centimetres
b) The large rectangle has dimensions 13 cm by 11 cm. Its area is:
A = 13 * 11 = 143 square centimetres
The unshaded part has dimensions 8 cm by 2 cm. Its area is:
a = 8 * 2 = 16 square centimetres
Therefore, the area of the shaded part is:
A - a = 143 - 16 = 127 square centimetres
6. The background area of the space not covered by the photograph is the area of the frame minus the area of the photograph.
The frame has dimensions 24 cm by 18 cm. Therefore, its area is:
A = 24 * 18 = 432 square centimetres
The photograph has dimensions 14 cm by 10 cm. Therefore, its area is:
a = 14 * 10 = 140 square centimetres
Therefore, the background area of the space not covered by the photograph is:
A - a = 432 - 140 = 292 square centimetres
8) The floor has dimensions 8 m by 4 m. The area of the floor is:
A = 8 * 4 = 32 square centimetres
Each square tile has dimensions 20 cm by 20 cm. In metres, that is 0.2 m by 0.2 m. The area of each tile is:
a = 0.2 * 0.2 = 0.04 square metres
The number of tiles that are needed is the area of the floor divided by the area of each tile:
A / a = 32 / 0.04 = 800 tiles
