This set of Aptitude Questions and Answers (MCQs) focuses on “Polygons – Set 2”.
1. How many sides does a polygon having sum of interior angles as 4140 will have?
a) 24
b) 26
c) 25
d) 27
View Answer
Explanation: Given,
Sum of interior angles = 4140
Let the number of sides be n.
➩ 4140 = (n – 2) * 180
➩ 4140 = 180n – 360
➩ 4140 + 360 = 180n
➩ 4500 = 180n
➩ 4500 / 180 = n
➩ n = 25
2. What will be the measure of each interior angle of a regular octagon in degrees?
a) 135
b) 140
c) 132
d) 125
View Answer
Explanation: Given,
As we know,
Sum of interior angles of polygon of side n = (n – 2) * 180
For a regular octagon n = 8
Sum of interior angles = (8 – 2) * 180
= 6 * 180
= 1080
Now the hexagon will have 6 equal interior angles thus,
Each interior angle = 1080 / 8
= 135 degrees
3. What will be the area (in sq. m) of a regular pentagon having side length as 1m long?
a) 1.32
b) 1.71
c) 1.83
d) 1.54
View Answer
Explanation: As we know,
Area of a pentagon = \(\frac {1}{4}\) (5(5 + 2√5))1/2 * z2
Given z = 1 m
Area = \(\frac {1}{4}\) (5(5 + 2√5))1/2 * (1)2
= \(\frac {1}{4}\) (5(5 + 2√5))1/2 * 1
= \(\frac {1}{4}\) (5(5 + 2(2.23))1/2
= \(\frac {1}{4}\) (5(5 + 4.46))1/2
= \(\frac {1}{4}\) (5(9.46))1/2
= \(\frac {1}{4}\) (47.3)1/2
= \(\frac {1}{4}\) (6.87)
= 1.71 m2
4. What will be the area (in sq. m) of a kite shaped field having shorter diagonal as 9 m and longer diagonal as 14 m long?
a) 63
b) 126
c) 31.5
d) 70
View Answer
Explanation: Given,
p = 9m, q = 14m
Area of kite = (p * q) / 2
= (9 * 14) / 2
= 126 / 2
= 63 m2
5. Which of the following is the correct expression representing the area of a regular octagon having side as ‘a’?
a) 4 * ( 1 + √2) * a2
b) 4 * (1 + √2) * a3
c) 2 * (1 + √2) * a2
d) 2 * (1 + √2) * a3
View Answer
Explanation: Given,
Side = a
Formula for area of a regular octagon = 2 * (1 + √2) * a2
6. The diagonal of a quadrilateral shaped field is 25 m and the perpendiculars dropped on it from the remaining opposite vertices are 8 m and 12 m. What will be the area (in sq. m) of this field?
a) 350
b) 295
c) 275
d) 250
View Answer
Explanation: Given,
d = 25m, h1 = 8m, h2 = 12m
Area = (1 / 2) * d * (h1 + h2)
= (1 / 2) * 25 * (8 + 12)
= (1 / 2) * 25 * (20)
= 250 m2
7. If the width of a rectangle is 12 cm less than its length and its perimeter is 60 cm. What will be the width of this rectangle?
a) 9 cm
b) 21 cm
c) 18 cm
d) 12 cm
View Answer
Explanation: Given,
Perimeter = 60 cm
Let the width be w then length would be w + 12
Perimeter = 2 (l + b)
➩ 60 = 2 (w + 12 + w)
➩ 60 = 2 (2w + 12)
➩ 60 = 4w + 24
➩ 36 = 4w
➩ 9 = w
8. What will be the area (in sq. cm) of an isosceles triangle having base as 24 cm and height as 28 cm long?
a) 325
b) 357
c) 336
d) 380
View Answer
Explanation: Given,
b = 24 cm, h = 28 cm
Area = \(\frac {1}{2}\) * b * h
= \(\frac {1}{2}\) * 24 * 28
= 336 cm2
9. What will be the area (in sq. m) of a square field having diagonal as 20 m?
a) 100
b) 200
c) 400
d) 250
View Answer
Explanation: Given,
d = 20 m
Area of square = d2 / 2
= 202 / 2
= 400 / 2
= 200 m2
10. How many diagonals does a heptagon has?
a) 14
b) 28
c) 18
d) 25
View Answer
Explanation: Given,
Number of sides n = 7
Number of diagonals = (n * (n – 3)) / 2
= (7 * (7 – 3)) / 2
= (7 * 4) / 2
= 14
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