1. Find the area, in square metres, of the trapezium whose bases and altitudes are as under:
(i) bases = 12 dm and 20 dm, altitude = 10 dm
(ii) bases = 28 cm and 3 dm, altitude = 25 cm
(iii) bases = 8 m and 60 dm, altitude = 40 dm
(iv) bases = 150 cm and 30 dm, altitude = 9 dm
Solution:
(i) Given that,
Length of bases of trapezium = 12 dm and 20 dm
Length of altitude = 10 dm
We know that, 10 dm = 1 m
∴ Length of bases in m = 1.2 m and 2 m
Similarly, length of altitude in m = 1 m
Area of trapezium = 1/2 (Sum of lengths of parallel sides) × altitude
Area of trapezium = 1/2 (1.2 + 2.0) × 1
Area of trapezium = 1/2 × 3.2 = 1.6
So, Area of trapezium = 1.6m2
(ii) Given that,
Length of bases of trapezium = 28 cm and 3 dm
Length of altitude = 25 cm
We know that, 10 dm = 1 m
∴ Length of bases in m = 0.28 m and 0.3 m
Similarly, length of altitude in m = 0.25 m
Area of trapezium = 1/2 (Sum of lengths of parallel sides) × altitude
Area of trapezium = 1/2 (0.28 + 0.3) × 0.25
Area of trapezium = 1/2 × 0.58× 0.25 = 0.0725
So, Area of trapezium = 0.0725m2
(iii) Given that,
Length of bases of trapezium = 8 m and 60 dm
Length of altitude = 40 dm
We know that, 10 dm = 1 m
∴ Length of bases in m = 8 m and 6 m
Similarly, length of altitude in m = 4 m
Area of trapezium = 1/2 (Sum of lengths of parallel sides) × altitude
Area of trapezium = 1/2 (8 + 6) × 4
Area of trapezium = 1/2 × 56 = 28
So, Area of trapezium = 28m2
(iv) Given that,
Length of bases of trapezium = 150 cm and 30 dm
Length of altitude = 9 dm
We know that, 10 dm = 1 m
∴ Length of bases in m = 1.5 m and 3 m
Similarly, length of altitude in m = 0.9 m
Area of trapezium = 1/2 (Sum of lengths of parallel sides) × altitude
Area of trapezium = 1/2 (1.5 + 3) × 0.9
Area of trapezium = 1/2 × 4.5 × 0.9 = 2.025
So, Area of trapezium = 2.025m2
2. Find the area of trapezium with base 15 cm and height 8 cm, if the side parallel to the given base is 9 cm long.
Solution:
Given that,
Length of bases of trapezium = 15 cm and 9 cm
Length of altitude = 8 cm
We know that,
Area of trapezium = 1/2 (Sum of lengths of parallel sides) × altitude
Area of trapezium = 1/2 (15 + 9) × 8
Area of trapezium = 1/2 × 192 = 96
So, Area of trapezium = 96m2
3. Find the area of a trapezium whose parallel sides are of length 16 dm and 22 dm and whose height is 12 dm.
Solution:
Given that,
Length of bases of trapezium = 16 dm and 22 dm
Length of altitude = 12 dm
We know that, 10 dm = 1 m
∴ Length of bases in m = 1.6 m and 2.2 m
Similarly, length of altitude in m = 1.2 m
Area of trapezium = 1/2 (Sum of lengths of parallel sides) × altitude
Area of trapezium = 1/2 (1.6 + 2.2) × 1.2
Area of trapezium = 1/2 × 3.8 × 1.2 = 2.28
So, Area of trapezium = 2.28m2
4. Find the height of a trapezium, the sum of the lengths of whose bases (parallel sides) is 60 cm and whose area is 600 cm2.
Solution:
Given that,
Length of bases of trapezium = 60 cm
Area = 600 cm2
We know that,
Area of trapezium = 1/2 (Sum of lengths of parallel sides) × altitude
600 = 1/2 (60) × altitude
600 = 30 × altitude
Which implies, altitude = 600/30 = 20
∴ Length of altitude is 20 cm
5. Find the altitude of a trapezium whose area is 65 cm2 and whose base are 13 cm and 26 cm.
Solution:
Given that,
Length of bases of trapezium = 13 cm and 26 cm
Area = 65 cm2
We know that,
Area of trapezium = 1/2 (Sum of lengths of parallel sides) × altitude
65 = 1/2 (13 + 26) × altitude
65 = 39/2 × altitude
Which implies, altitude = (65×2) /39 = 130/39 = 10/3
∴ Length of altitude = 10/3 cm
6. Find the sum of the lengths of the bases of a trapezium whose area is 4.2 m2 and whose height is 280 cm.
Solution:
Given that,
Height of trapezium = 280 cm = 2.8m
Area = 4.2 m2
We know that,
Area of trapezium = 1/2 (Sum of lengths of parallel sides) × altitude                   To calculate the length of parallel sides we can rewrite the above equation as,
Sum of lengths of parallel sides = (2 × Area) / altitude
Sum of lengths of parallel sides = (2 × 4.2) / 2.8 = 8.4/2.8 = 3
∴ Sum of lengths of parallel sides = 3 m
