(English Medium) ICSE Class 9 - CISCE Question Bank Solutions

Find the area of a triangle whose sides are 18 cm, 24 cm, and 30 cm. Also, find the length of altitude corresponding to the largest side of the triangle.

AD is altitude of an isosceles triangle ABC in which AB = AC = 30 cm and BC = 36 cm. A point O is marked on AD in such a way that ∠BOC = 90^o. Find the area of quadrilateral ABOC.

If the difference between the sides of a right-angled triangle is 3 cm and its area is 54 cm²; find its perimeter.

In triangle ABC; angle A = 90^o, side AB = x cm, AC = (x + 5) cm and area = 150 cm². Find the sides of the triangle.

Calculate the area and the height of an equilateral triangle whose perimeter is 60 cm.

The length of the sides of a triangle are in the ratio 3: 4: 5. Find the area of the triangle if its perimeter is 144 cm.

ABC is a triangle in which AB = AC = 4 cm and ∠A = 90°. Calculate:
(i) The area of ΔABC,
(ii) The length of the perpendicular from A to BC.

The area of an equilateral triangle is 36`sqrt3` sq. cm. Find its perimeter.

Find the area of an isosceles triangle with perimeter is 36 cm and the base is 16 cm.

The sides of a triangular field are in the ratio 5: 3: 4 and its perimeter is 180 m. Find:

1. its area.
2. the altitude of the triangle corresponding to its largest side.
3. the cost of leveling the field at the rate of Rs. 10 per square meter.

The base of a triangular field is three times its height. If the cost of cultivating the field at ₹ 36.72 per 100 m² is ₹ 49,572; find its base and height.

Find the area and the perimeter of quadrilateral ABCD, given below; if AB = 8 cm, AD = 10 cm, BD = 12 cm, DC = 13 cm and ∠DBC = 90°.

The given figure shows a right-angled triangle ABC and an equilateral triangle BCD. Find the area of the shaded portion.

The perimeter of a triangle is 450 m and its side are in the ratio 12: 5: 13. Find the area of the triangle.

The length, breadth and height of a rectangular solid are in the ratio 5 : 4 : 2. If the total surface area is 1216 cm², find the length, the breadth and the height of the solid.

The dimensions of a Cinema Hall are 100 m, 60 m, and 15 m. How many persons can sit in the hall if each requires 150 m³ of air? 

A closed rectangular box is made of wood of 1.5 cm thickness. The exterior length and breadth are respectively 78 cm and 19 cm, and the capacity of the box is 15 cubic decimeters. Calculate the exterior height of the box.

75 persons can sleep in a room 25 m by 9.6 m. If each person requires 16 m³ of the air; find the height of the room. 

The external dimensions of a closed wooden box are 27 cm, 19 cm, and 11 cm. If the thickness of the wood in the box is 1.5 cm; find:

1. The volume of the wood in the box;
2. The cost of the box, if wood costs Rs. 1.20 per cm³;
3. A number of 4 cm cubes that could be placed into the box.

Given: 4 sin θ = 3 cos θ ; find the value of:
(i) sin θ (ii) cos θ
(iii) cot² θ - cosec² θ .
(iv) 4 cos²θ- 3 sin²θ+2