Answer:
a) 8.8 square centimetres
b) 31.8 square centimetres
c) (3a + 12) square centimetres
d) Area = (2b + 2c + 4) square centimetres
Explanation:
a) We have to split the diagram into three separate rectangles as shown below.
The area of A:
Area = 5.3 * 1 = 5.3 square centimetres
The area of B:
Area = 3.3 * 1 = 3.3 square centimetres
The area of C:
Area = 2 * 1 = 2 square centimetres
The area of the shape is the sum of the areas of the three shapes:
Area = 5.3 + 3.3 + 2 = 8.8 square centimetres
b) We have to split the diagram into two separate rectangles as shown below.
Note:(The diagram has conflicting values for 2.6 and 2.1 but I went with 2.6 as it seems more feasible in the diagram)
The area of A:
Area = 3 * 2.6 = 7.8 square centimetres
The area of B:
Area = 6 * 4 = 24 square centimetres
The area of the shape is the sum of the areas of the two shapes:
Area = 7.8 + 24 = 31.8 square centimetres
c) The shape is a rectangle and so its area is:
Area = 3 * (a + 4) = (3a + 12) square centimetres
d) The shape is a trapezium and so its area is:
Area = 0.5(A + B)H
where A = c cm
B = b + 2 cm
H = 4 cm
The area of the shape is therefore:
Area = 0.5 * (c + b + 2) * 4
Area = 2 * (b + c + 2)
Area = (2b + 2c + 4) square centimetres