Page 274 - Start Up Mathematics_8 (Non CCE)

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Example 13: The area of a trapezium is 720 cm . If the parallel sides are 7 cm and 13 cm long, find the
distance between them. 7 cm
Solution: Area of trapezium = 720 cm 2
Length of parallel sides = 7 cm and 13 cm ?
Let the distance between the parallel sides be x cm. 13 cm
1
Area of trapezium = × (Sum of lengths of parallel sides) × (Distance between them)
2
1
720 = × (7 + 13) × x
2
1
fi × 20 × x = 720 fi 10 × x = 720
2
720
fi x = = 72 cm
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Example 14: The ratio of the length of the parallel sides of a trapezium is 4 : 1. The distance between them
2
is 10 cm. If the area of the trapezium is 500 cm , find the lengths of the parallel sides.
Solution: Let the length of the two parallel sides be 4x and x respectively.
Distance between them = 10 cm
Area of trapezium = 500 cm 2
1
Area of trapezium = × (Sum of lengths of parallel sides) × (Distance between them)
2
1 1
fi 500 = × (4x + x) × 10 fi × 5x × 10 = 500
2 2
fi 5x × 5 = 500 fi 25x = 500 fi x = 500 = 20
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Hence, the lengths of the two parallel sides are 4 × 20 cm and 20 cm, i.e., 80 cm and 20 cm.

Example 15: Mohan wants to buy a trapezium-shaped field. Its side along the river is parallel to and twice
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the side along the road. If the area of this field is 10,500 m and the perpendicular distance
between the two parallel sides is 100 m, find the length of the side along the river.
(NCERT)
Solution: Area of the field = 10,500 m 2
Distance between parallel sides = 100 m

Let the length of the side along the road be x m.
Then, the length of the side along the river = 2x m
1
Area of trapezium (field) = × (Sum of lengths of parallel sides) × (Distance between them)
2
1 Road
fi 10,500 = × (x + 2x) × 100
2
1
fi × 3x × 100 = 10,500 fi 3x × 50 = 10,500 100 m
2
10 500,
fi 3x = = 210 fi 3x = 210
50 River
210
fi x = = 70
3
\ The length of the side along the river = 2x m = (2 × 70) m = 140 m

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