Problems on Areas : Aptitude Test

• Important Mensuration Formulas

1.

Of the two square fields, the area of the one is 1 hectare, while anothe one is broader by 1%. There differences in area is:

A.) 200 m
B.) 201 m
C.) 201 m2
D.) None of these

Area of one square field = 10000 m2
10000 × 1 = 10000
Side of this field = √10000 m = 100 m
Side of another square = 101 m
Difference of areas = [ 1012 - 1002 ] m2
[101+100][101-100] m2
(201)(1) m2 = 201 m2

2.

Find the cost of carpenting a room 13 m long and 9 m broad with a carpet 100 Cm broad at the rate of Rs.20 per meter.

A.) 117 m
B.) 107 m
C.) 116 m
D.) 117 m2

Area of the carper = Area of the room
= 13 × 9 => 117 m2
Breadth of the carpet = 100 cm = 1m
Length of carpet = Area/Breadth => 117/1 = 177 m.

3.

A girl walking at the rate of 9 Km per hour crosses a square field diagonally in 12 seconds. The area of the field is:

A.) 460 sq.m
B.) 600 sq.m
C.) 510 sq.m
D.) 450 sq.m

Distance covered in (9×1000)/(3600) × 12 = 30 m
Diagonal of squarre field = 30 m.
area of square field = 302/2
= 900/2 = 450 Sq.m

4.

The inner circumference of a circle race track 18 m wide is 880 m. Find the radius of the outer circle.

A.) 140 cm
B.) 150 m
C.) 140 m
D.) None of these

Let inner radius be r metres
Then 2πr = 640
2 × 22/7 r = 880
44/7 r = 880
r = 880 × 7/44 = 140 m

5.

The perimeter of a square circumscribed about a ciecle of radius r is:

A.) 12 r
B.) 16 r
C.) 64 r
D.) 8 r

Each side of the square = 2r
Perimeter of the square = (4×2r) = 8r

6.

The area of a square field is 4802 m2 the length of its diagonal is:

A.) 94 m
B.) 96 m
C.) 98 m
D.) None of these

Let the diagonal be d metres,
Then 1/2 d2 = 4802
d2 = 9604
d = √9604
d = 98 m

7.

The diagonal of a rhombus are 65 m and 60 m. Its area is:

A.) 1950 cm^3
B.) 1950 cm^2
C.) 1960 cm^2
D.) 1960 cm^3

Area of the rhombus = 1/2 d1d2 = ( 1/2 × 65 × 60 ) cm2
= 65 × 30 = 1950 cm2

8.

The diagonal of a square is 40 m. The area of the square is:

A.) 800 m2
B.) 800 m3
C.) 750 m2
D.) None of these

Arear = 1/2 × ( diagonal )2
= ( 1/2 × 40 × 40 )m2
= 1600/2 = 800 m2

9.

The area of the largest triangle that can be inscribed in a semicircle pf rasius r Cm, is:

A.) r3 Cm2
B.) r2 Cm3
C.) r2 Cm2
D.) r3 Cm3

Area of the largest triangle = (1/2 × 2r × r) cm2 = r2 cm2

10.

Find the area of the sector whose are is making an angle of 90° at the center of a circle of radius 3.2 Cm.

A.) 46.32 Sq.cm
B.) 54.32 Sq.cm
C.) 56.22 Sq.cm
D.) 56.32 Sq.Cm

Area of the sector = 90/360 × πr2
= 90/360 × 22/7 × 3.2 × 3.2
= (11 × 10.24)/2 = 112.64/2 = 56.32 Sq.Cm

• Important Mensuration Formulas

11.

If the radius of a circle decreased by 50% its area is decreased by:

A.) 75%
B.) 50%
C.) 85%
D.) 65%

Original area = πr2
New area = π(r/2)2 = (πr2)/4
Reduction in area = [(πr2 - (πr2)/4]2 = (3πr2)/4
Reduction percent = ((3πr2)/4 × 1/(πr2 × 100) % = 75%

12.

A rectangular room 14 m long, 12 m broad is surrounded by a varandah, 3 m wide. Find the area of the varandah?

A.) 190 m2
B.) 170 m2
C.) 180 m3
D.) 180 m2

Area of varandah = (l+b+2p)2p
= (14 + 12 + 6 ) 6
= 180 m2

13.

The area of the largest circle that can be drawn inside a square of side 28 Cm in length is:

A.) 616 Cm3
B.) 626 Cm2
C.) 619 Cm2
D.) 616 Cm2

Radius of required circle = 14 Cm
its area = 22/7 × 14 × 14
44 × 14 = 616 Cm2

14.

Area of four walls of a room is 99 m2. The length and breadth of the room are 7.5 m and 3.5m respectively. The height of the room is:

A.) 4.5 Cm
B.) 5.5 m
C.) 4.5 m
D.) 5.5 Cm