Page 230 - ICSE Math 8

Example 14: In a trapezium, two parallel sides and the perpendicular distance between them are in the ratio
2
5 : 7 : 4. If the area of the trapezium is 384 cm , find its height.
Solution: Let the lengths of parallel sides be 5x cm and 7x cm and height be 4x cm.
1
Area of trapezium = × (sum of the lengths of its parallel sides) × height
2
1 1
∴ 384 = × (5x + 7x) × 4x ⇒ 384 = × 12x × 4x
2
2
384
2
2
2
⇒ 384 = 24x ⇒ 24 = x ⇒ 16 = x ⇒ x = 4
∴ The height of the trapezium is 4x cm = 4 × 4 cm = 16 cm.

EXERCISE 21.3

1. Find the area of a parallelogram with base 15 cm and height 11.5 cm.
2. A parallelogram has sides 18 cm and 15 cm. If the distance between its longer sides is 5 cm, find the
distance between its shorter sides.
3. The length of diagonals of a rhombus are 6 cm and 8 cm. Find its area.
4. The parallel sides of a trapezium are 15 cm and 12 cm. Find the area of the trapezium, if its height is
8 cm.
5. A rhombus with side 10 m has one diagonal of length 16 m. Find the length of the other diagonal and its
area.
6. The parallel sides of a trapezium are in the ratio 5 : 7. If the distance between the parallel sides is 18 cm
2
and its area is 540 cm , find the length of the parallel sides.
7. One of the parallel sides of a trapezium is 32 cm, the distance between the parallel sides is
2
24 cm and its area is 720 cm . Find the length of the other parallel side.
8. The adjacent sides of a parallelogram are 24 cm and 10 cm and the length of one of its diagonals is
26 cm. Find the area of the parallelogram.
9. Two parallel sides of a trapezium and the distance between them are in the ratio 4 : 3 : 2. If the area of
2
the trapezium is 1,372 cm , find its height.
2
10. The base of a parallelogram is thrice its height. If the area of the parallelogram is 243 cm , find its base
and height.
A B
11. ABCD is a trapezium in which AB || DC, AD ⊥ DC, AB = 23 cm,
BC = 13 cm and DC = 28 cm. Find the area of the trapezium.
D C
12. Find the area of the shaded region for each of the following.

(a) D 16 cm C (b) F E

10 cm D 5 cm C
24 cm
10 cm
A B
3 cm E F 3 cm
22 cm A 18 cm B
13. A floor of a building consists of 2,500 tiles. All the tiles are rhombus-shaped with diagonals
40 cm and 25 cm. Find the total cost of polishing the floor at the rate of ` 8 per square metre.

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