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

Answer»

(i) Area of trapezium = \(\frac{1}{2}\)(sum of lengths of parallel sides) x altitude

Length of bases of trapezium = 12 dm and 20 dm

10 dm = 1 m

Therefore length of bases in m = 1.2 m and 2 m

Similarly length of altitude in m = 1 m

Area of trapezium = \(\frac{1}{2}\)(1.2 + 2.0) x 1

Area of trapezium = \(\frac{1}{2}\)x 3.2 - 1.6 m2

(ii) Area of trapezium = \(\frac{1}{2}\)(sum of lengths of parallel sides) x altitude

Length of bases of trapezium = 28 cm and 3 dm

10 dm = 1 m

Therefore length of bases in m = 0.28 m and 0.3 m

Similarly length of altitude in m = 0.25 m

Area of trapezium = \(\frac{1}{2}\)(0.28 + 0.3) x 0.25

Area of trapezium = \(\frac{1}{2}\) x 0.58 x 0.25 = 0.0725 m2

(iii) Area of trapezium = \(\frac{1}{2}\)(sum of lengths of parallel sides) x altitude

Length of bases of trapezium = 8 m and 60 dm

10 dm = 1 m

Therefore length of bases in m = 8 m and 6 m

Similarly length of altitude in m = 4 m

Area of trapezium = \(\frac{1}{2}\)(8 + 6) x 4

Area of trapezium = \(\frac{1}{2}\)x 14 x 4 = 28 m2

(iv) Area of trapezium = \(\frac{1}{2}\)(sum of lengths of parallel sides) x altitude

Length of bases of trapezium = 150 cm and 30 dm

10 dm = 1 m

Therefore length of bases in m = 1.5 m and 3 m

Similarly length of altitude in m = 0.9 m

Area of trapezium = \(\frac{1}{2}\)(1.5 + 3) x 0.9

Area of trapezium = \(\frac{1}{2}\)x 4.5 x 0.9 = 2.025 m2



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