Mensuration - I (Area and Perimeter)

 Measures of Length 

• 10 mm = 1 cm

• 10 cm = 1 decimetre 

• 10 decimetre = 1 m

• 10 m = 1 decametre 

• 10 decametre = 1 hectometre

• 10 hectometre = 1 kilometre

1. A wire can be bent in the form of a circle of radius 28 cm. If it is bent in the form of a square,  then what will be its area? (Ans.1936cm²)

2. The perimeter of a semicircular area is 18 cm, then the radius is :________ (Ans.7/2 cm)

3. If the four equal circles of radius 3 cm touch each other externally,  then the area of the region bounded by the four circles is _____.(Ans.  9(4 - π) sq. cm)

4. At the centres of two circles,  two arcs of equal length subtend angles of 60° and 75° respectively.  The ratio of the radii of the two circles is _______. (Ans. 5 : 4)

5. Area of the incircle of an equilateral triangle with side 6 cm is ______. (Ans. 3π sq. cm)

6. A rectangular room can be partitioned into two equal square rooms by a partition 7 metres long.  What is the area of rectangular room in square metres? (Ans. 98 m²)

7. If the perimeter of a rectangle and a square,  each is equal to 80 cm and the difference of their areas is 100 sq. cm, the sides of the rectangle are :______? (Ans. 30 cm & 10 cm)

8. The two parallel sides of a trapezium are 1.5 m and 2.5 m respectively.  If the perpendicular distance between them is 6.5 m, the area of the trapezium is: (Ans. 13 m²)

Previous Years Questions 

1. What is the least number of square tiles required to pave the floor of a room 15 m 17 cm and 9 m 2 cm broad? (Ans. 814)

2. The sides of a triangle are 3 cm, 4 cm and 5 cm. The area of the triangle formed by joining the midpoints of the sides of this triangle is: (Ans. 3/2 cm²)

3. An equilateral triangle is described on the diagonal of a square.  What is the ratio of the area of the triangle to that of the square? ( Ans. √3 : 2)

4. If the side of an equilateral triangle is decreased by 20%, its area is decreased by : (Ans. 36%)

Assignments

1. The length of a rectangle is increased by 60%. By what percent would the width have to be decreased to maintain the same area?

A. 75/2%  

B. 60% 

C. 75% 

D. 200/3%

2. The ratio of the areas of the incircle and the cir-cumcircle of a square is :

A. 1:2

B. 2:3 

C. 3:4

D. 4:5

3. The ratio of sides of a triangle is 3:4:5 and area of the triangle is 72 square unit. Then the area of an equilateral triangle whose perimeter is same as that of the previous triangle is

A. 32√3 square unit 

B. 96 square unit

C. 48 √3 square unit

D. 60 √3 square unit

4. The perimeter of a semicircular path is 36 m. Find the area of this semicircular path.

A. 42sq.m

B. 63 sq.m

C. 54 sq. m

D. 77 sq. m