Area Questions and Answers – Polygons – Set 2

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

Answer: c
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

Answer: a
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

Answer: b
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
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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

Answer: a
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

Answer: c
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

Answer: d
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

Answer: a
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
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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

Answer: c
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

Answer: b
Explanation: Given,
d = 20 m
Area of square = d2 / 2
= 202 / 2
= 400 / 2
= 200 m2
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10. How many diagonals does a heptagon has?
a) 14
b) 28
c) 18
d) 25
View Answer

Answer: a
Explanation: Given,
Number of sides n = 7
Number of diagonals = (n * (n – 3)) / 2
= (7 * (7 – 3)) / 2
= (7 * 4) / 2
= 14

To practice all aptitude questions, please visit “1000+ Quantitative Aptitude Questions”, “1000+ Logical Reasoning Questions”, and “Data Interpretation Questions”.

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Manish Bhojasia - Founder & CTO at Sanfoundry
Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He lives in Bangalore, and focuses on development of Linux Kernel, SAN Technologies, Advanced C, Data Structures & Alogrithms. Stay connected with him at LinkedIn.

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