Area Problems Quiz 4 for RRB Group D, RRB ALP, SSC CGL Tier 1, CGL Tier 2, SSC CHSL

Directions: Study the following questions carefully and choose the right answer.
1
A piece of wire 78 cm long is bent in the form of an isosceles triangle. If the ratio of one of the equal sides to the base is 5 : 3, then what is the length of the base?
» Explain it
B
Let the sides of isosceles triangle is 5x, 5x and 3x cm respectively.

By given condition,

Perimeter of isosceles triangle = Length of wire

⇒ 5x + 5x + 3x = 78

⇒ 13x = 78

⇒ x = 6 cm

∴  Length of base = 3x = 3 × 6 = 18 cm

Hence, option B is correct.


2
The length of a minute hand of a wall clock is 9 cm. What is the area swept (in cm2) by the minute hand in 20 min ? (take π = 3.14)
» Explain it
B
Given, r = 9 cm

The angle made by the minute hand in 20 min, Θ = 120°

∴  The area swept by the minute hand in 20 min

Θ  × πr2
360°

120°  × 3.14 × 9 × 9
360°

= 84.78 cm2

Hence, opton B is correct.

3
If the area of a ΔABC is equal to area of square of sde length 6 cm, then what is the length of the altitude to AB, where AB = 9 cm ?
» Explain it
D
Given, AB = 9 cm

Let the length of altitude to AB = l cm

By given condition,

Area of ΔABC = Area of square

∴   1  × Base × Altitude = (Side length)2
2

⇒   1  × 9 × l = 36
2

⇒  l =  36 × 2  = 8 cm
9

Hence, option D is correct.

4
What is the area of an equilateral triangle having altitude equal to 2√3 cm?
» Explain it
D
We know that,

altitude of an equilateral triangle 

3
a
2

⇒  2
3
 = 
3
a
2

⇒  a = 4 cm

∴  Area of equilateral triangle

3
a2 = 
3
 × (4)2 = 4
3
 cm2
4 4

Hence, option D is correct.

5
If a circle circumscribes a rectangle with side 16 cm and 12 cm, then what is the area of the circle ?
» Explain it
C

In right-angled ΔABC,
 
AC =  AB2 + BC2

162 + 122  =  400  = 20 cm

Diameter of circumcircle = 20 cm

∴  Radius of circumcircle (r) = 10 cm

Area of circumcircle = πr2 = π × (10)2 = 100π cm2

Hence, option C is correct.