Mensuration Questions: Overview, Questions, Preparation

Menstruation deals with geometrical figures and their parameters. We can calculate various measurements of geometric figures such as square, rectangle, circle, sphere, and cube through the study of mensuration.

Mensuration
The formulas to calculate various parameters of geometric figures are given below.

The topic- mensuration questions are a part of the chapter- circles and chapter- surface areas and volumes in the syllabus of class 10. These chapters are important parts of the syllabus and carry a weightage of around 10-12 marks in the examination.

1.A hall that is in the shape of a trapezium has an area of 60 m2, the distance between its two parallel sides is 10 m and the length of one of the parallel sides is 4 m. What is the value of the unknown side?

Solution:

According to the question, the length of one of the parallel sides of the hall is a = 4m,  and the value of height h = 10 m.
We know that the area of this hall = 60 m2.
Formula for trapezium = ½  h (a + b).
So, 60 = ½  × 10 × (4 + b) = 5 x (4 + b)
=> b= 12- 4= 8m.

2. If it is known that the area of a rhombus is 360 cm2 and the value of one diagonal is 24 cm. Find the value associated with the other diagonal of this figure.
Solution:
Given, the length of one diagonal = 24 cm= l1
Let the other diagonal be l2
The area of the rhombus= Ar= 320.
Area of rhombus is given by- Ar= Area= ½ x (diameter 1 x diameter 2)
=> Ar = ½ x (l1 x l2)= ½ x 24 x l2
=> 360= 12 x l2 => l2= 30 cm.
So, the value of another diagonal of this figure is 30cm.

3. A  cubical room has dimensions 14 m × 10 m × 6 m. What will be the price of covering all the walls in the paint if the cost of paint per metre square is 5 rupees. 
Solution:
Area of the walls of the cubical = Perimeter of the base × Height of the room 
= 2 (l + b) × h = 2 (14 + 10) × 6 = 2 × 24 × 6 = 288 m2
The total price of painting on the walls of the cubicle = Rs. (288 × 5) = Rs. 1440