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Area Problems Quiz 4 for RRB Group D, RRB ALP, SSC CGL Tier 1, CGL Tier 2, SSC CHSL
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Directions: Study the following questions carefully and choose the right answer.
Important for :
CDSE
CGL Tier 2
CGLTier 1
Railways
SSC 10+2
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?
A
16 cm
B
18 cm
C
20 cm
D
30 cm
» Explain it
Correct Option:
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.
1
A
B
C
D
» Explain it
सही विकल्प :
B
B
2
The length of a minute hand of a wall clock is 9 cm. What is the area swept (in cm
^{2}
) by the minute hand in 20 min ? (take π = 3.14)
A
88.78
B
84.78
C
67.74
D
57.78
» Explain it
Correct Option:
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
× πr
^{2}
360°
=
120°
× 3.14 × 9 × 9
360°
= 84.78 cm
^{2}
Hence, opton B is correct.
2
A
B
C
D
» Explain it
सही विकल्प :
B
B
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 ?
A
18 cm
B
14 cm
C
12 cm
D
8 cm
» Explain it
Correct Option:
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.
3
A
B
C
D
» Explain it
सही विकल्प :
D
D
4
What is the area of an equilateral triangle having altitude equal to 2√3 cm?
A
√3 sq cm
B
2√3 sq cm
C
3√3 sq cm
D
4√3 sq cm
» Explain it
Correct Option:
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
a
^{2}
=
3
× (4)
^{2}
= 4
3
cm
^{2}
4
4
Hence, option D is correct.
4
A
B
C
D
» Explain it
सही विकल्प :
D
D
5
If a circle circumscribes a rectangle with side 16 cm and 12 cm, then what is the area of the circle ?
A
48π sq cm
B
50π sq cm
C
100π sq cm
D
200π sq cm
» Explain it
Correct Option:
C
In right-angled ΔABC,
AC =
AB
^{2}
+ BC
^{2}
=
16
^{2}
+ 12
^{2}
=
400
= 20 cm
Diameter of circumcircle = 20 cm
∴ Radius of circumcircle (r) = 10 cm
Area of circumcircle = πr
^{2}
= π × (10)
^{2}
= 100π cm
^{2}
Hence, option C is correct.
5
A
B
C
D
» Explain it
सही विकल्प :
C
C
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