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

The perimeter of a rhombus is 46 cm. If the height of the rhombus is 8 cm; find its area.

The perimeter of a rhombus is 52 cm. If one diagonal is 24 cm; find:
(i) The length of its other diagonal,
(ii) Its area.

The length of a rectangular verandah is 3 m more than its breadth. The numerical value of its area is equal to the numerical value of its perimeter.

(i) Taking x as the breadth of the verandah, write an equation in x that represents the above statement

(ii) Solve the equation obtained in (i) above and hence find the dimensions of the verandah. 

The area of a rhombus is 216 sq. cm. If it's one diagonal is 24 cm; find:
(i) Length of its other diagonal,
(ii) Length of its side,
(iii) The perimeter of the rhombus.

Two adjacent sides of a parallelogram are 24 cm and 18 cm. If the distance between the longer sides is 12 cm; find the distance between the shorter sides.

The diagram, given below, shows two paths drawn inside a rectangular field 80 m long and 45 m wide. The widths of the two paths are 8 m and 15 m as shown. Find the area of the shaded portion. 

Two adjacent sides of a parallelogram are 28 cm and 26 cm. If one diagonal of it is 30 cm long; find the area of the parallelogram. Also, find the distance between its shorter sides.

The rate for a 1.20 m wide carpet is Rs. 40 per meter; find the cost of covering a hall 45 m long and 32 m wide with this carpet. Also, find the cost of carpeting the same hall if the carpet, 80 wide, is at Rs. 25. Per meter. 

A floor that measures 15 m x 8 m is to be laid with tiles measuring 50 cm x 25 cm. Find the number of tiles required.
Further, if a carpet is laid on the floor so that a space of 1 m exists between its edges and the edges of the floor, what fraction of the floor is left uncovered?

The shaded region of the given diagram represents the lawn in the form of a house. On the three sides of the lawn, there are flowerbeds having a uniform width of 2 m.

(i) Find the length and the breadth of the lawn.
(ii) Hence, or otherwise, find the area of the flower-beds.

Find the area and perimeter of a square plot of land, the length of whose diagonal is 15 meters. Given your answer correct to 2 places of decimals. 

A triangle and a parallelogram have the same base and the same area. If the side of the triangle is 26 cm, 28 cm, and 30 cm and the parallelogram stands on the base 28 cm, find the height of the parallelogram.

Using the information in the following figure, find its area.

Sum of the areas of two squares is 400 cm². If the difference of their perimeters is 16 cm, find the sides of the two squares. 

Find the area and the perimeter of a square with diagonal 24 cm. [Take √2 = 1.41 ] 

The perimeter of a semicircular plate is 108 cm. find its area. 

Evaluate: `(tan 47°)/(cot 43°)`

Evaluate: `(cot54°)/(tan36°) + (tan20°)/(cot70°)-2`

Evaluate: `(2tan53°)/(cot 37°)-(cot 80°)/(tan 10°)`

Show that: tan 10° tan 15° tan 75° tan 80° = 1.