S Chand ICSE Mathematics Class 9 Solution Sixteenth Chapter Area of Plane Figures Exercise 16C (O.P. Malhotra, S.K. Gupta, Anubhuti Gangal)
(1) Find the area of a parallelogram whose base and height are as given below:
|Base||8 cm||2.8 cm||12 mm||6.5 m|
|Height||3 cm||5 cm||8.7 mm||4.8 m|
Solution: (1) (i) Area = Base x height
= 8 x 3
= 24 cm2
(ii) Area = (2.8 x 5) cm2
= 14 cm2
(iii) Area = 12 x 8.7 mm2
= 104.4 mm2
(iv) Area = (6.5 x 4.8) m2
= 31.20 m2
(2) The area of a parallelogram is 1 ½ ares. Its base is 20 m. Find its height. (1 arc = 100 m2)
Solution: Area = (3/2 x 100) m
= ( 3 x 50) m2
= 150 m2
∴ 150 = 20 x h
h = 7.5 m
(3) In a parallelogram ABCD, AB = 8 cm, BC = 5 cm, perp. From A to DC = 3 cm. Find the length of the perp. drawn from B to AD.
(4) A parallelogram has side 34 cm and 20 cm. One of its diagonals is 42 cm. Calculate its area.
(5) ABCD is a parallelogram with side AB = 12 cm. Its diagonals AC and BD are the lengths 20 cm and 16 cm respectively. Find the area of || gm ABCD
(6) What is the area of a rhombus which has diagonals of 8 cm and 10 cm.
Solution: Area of rhombus = ½ x 8 x 10 cm2
= 40 cm2
(7) The area of a rhombus is 98 cm2. If one of its diagonals is 14 cm, what is the length of the other diagonal?
Solution: Area of rhombus = ½ x Product of diagonals
98 = ½ x 14 x a
Or, a = 14 cm
(8) PQRS is a rhombus.
(i) If it is given that PQ = 3 cm, calculate the perimeter of PQRS
(ii) If the height of the rhombus is 2.5 cm, calculate its area,
(iii) The diagonals of a rhombus are 8 cm and 6 cm respectively. Find its perimeter.
(i) PQ = 3 cm
∴ Perimeter = 4 x 3 cm
= 12 cm
(9) The sides of a rhombus are 5 cm each and one diagonal is 8 cm, calculate,
(i) The length of the other diagonal and
(ii) The area of the rhombus.
(i) Let, length of other diagonal is l cm
(10) In the given figure, ABCX is a rhombus of side 5 cm. angles BAD and ADC are right angles. If DC = 8 cm, calculate the area of ABCX.