Page 142 - Maths Skills - 7

140 Maths

Example 5: Find the area of a rhombus, whose diagonals are 34 cm and 26 cm.

Solution: Length of diagonals are 34 cm and 26 cm.
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\ Area of a rhombus = × (product of diagonals)
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1
= × (34 × 26) cm = 442 cm 2
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Example 6: One of the parallel sides of a trapezium is 25 cm more than the other. If
distance between the parallel sides is 20 cm and area is 1010 cm , then
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find both the parallel sides (Fig.).
Solution: Let one side be x cm. Then, the other parallel side will be (x + 25) cm.
Distance between them = 20 cm.

According to the condition,
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Area = × (Sum of parallel side) × (Distance between them)
2
1
⇒ 1010 cm = (x + x + 25 cm) × 20 cm
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1010 cm = (2x + 25 cm) × 10 cm
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⇒ (2x + 25) = 101 cm
⇒ 2x = 101 cm – 25 cm = 76 cm
\ x = 38 cm
\ The parallel sides are 38 cm and (38 + 25) = 63 cm

Exercise 8.4

1. Find the area of a parallelogram, one of whose sides is 8 cm and its distance from the opposite side is
6 cm.

2. The area of a parallelogram is 126 cm . If one side of a parallelogram is 14 cm, then find its distance
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from the opposite side.
3. The base of a parallelogram is 3 times its height. If the area of the parallelogram is 108 cm , find the
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height and base of the parallelogram.
4. The altitude of a parallelogram is twice its corresponding base. If the area of the parallelogram is
392 m , find the base and the altitude.
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5. The adjacent sides of a parallelogram are 35 cm and 25 cm. If the distance between the longer sides is
15 cm, find the distance between the shorter sides of the parallelogram.
6. An agriculture farm is in the form of a parallelogram with base 18 dam and altitude 9 dam. Find the
cost of watering the field at the rate of 75 paise per m .
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7. One side of a parallelogram is 22 cm and its corresponding altitude is 12
cm. If the height of the altitude to the adjacent side is 11 cm, find the length
of the adjacent side.
8. In Fig., ABCD is a parallelogram, AB = 18 cm, BC = 12 cm, AE ^ CD,
AF ^ BC and AE = 6.4 cm. Find the length of AF.