Questions On Polygons In Aptitude Tests

1. 5 DECEMBER 09 www.afterschoool.tk 1
QUESTIONS ON POLYGONS IN
APTITUDE TESTS
by :
DR. T.K. JAIN
AFTERSCHO☺OL
centre for social entrepreneurship
sivakamu veterinary hospital road
bikaner 334001 rajasthan, india
www.afterschoool.tk
mobile : 91+9414430763

2. 5 DECEMBER 09 www.afterschoool.tk 2
How many diagonals can be there
is a regular hexagon?
Formula = n (n-3) / 2
= 6(6-3) / 2
= 9 diagonals
answer

3. 5 DECEMBER 09 www.afterschoool.tk 3
How many sides are there in a
convex polygon having 27
diagonals?
27= n(n-3) / 2
n^2 -3n -54 =0
n^2 – 9n+6n-54
(n-9) (n+6)
thus answer is 9

4. 5 DECEMBER 09 www.afterschoool.tk 4
Exterior angle of a regular
polygon is 1/3
rd
of interior angle.
How many sides are there?
Let us assume interior angle = 3, ext. Angle
=1, thus interior angle = 3/4*180 = 135
fomula = (n-2) * 180/n = 135
n-2 = 3/4n, 1/4n = 2, n = 8
or ext. Angle = 45, divide 360/45 = 8

5. 5 DECEMBER 09 www.afterschoool.tk 5
ABCDE is regular pentagon,
diagonal AD divides angle CDE in
two parts. Find the ratio of angles
ADE to ADC
Exterior angle = 360 / 5 = 72, interior angle =
108
make a triangle, remaining two angles will be
36 each. Thus the ADE is 36 and ADC is 72
(remaining). Thus their ratio is 1:2. answer

6. 5 DECEMBER 09 www.afterschoool.tk 6
The difference between exterior angle of
(n-1) sided regular polygon and exterior
angle of (n+2) regular polygon is 6
degree, what is n?
Try and find.
12 and 15 give you exterior angles of 30 and
24, with difference of 6, thus n = 13.

7. 5 DECEMBER 09 www.afterschoool.tk 7
Ratio of interior angle to exterior
angle of a regular polygon is 7:2,
what is the number of sides?
Exterior angle = 2/(2+7) * 180 = 40
number of sides = 360 / 40 = 9 answer

8. 5 DECEMBER 09 www.afterschoool.tk 8
The ratio of number of sides of two
regular polygons is 1:2, ratio of measures
of their interior angles is 3:4, what is the
number of sides??
Hit and try
5 and 10 sides, will give you interior angles of
108 and 144, which have ratio of 3:4. answer

9. 5 DECEMBER 09 www.afterschoool.tk 9
Measure of an angle X is twice its
supplementary angle, find the
angle X?
Supplementary = which adds up to 180 degree.
Thus if supplentary is W, angle X is 2W
3W = 180, W = 60
X = 120 answer

10. 5 DECEMBER 09 www.afterschoool.tk 10
Two supplementary angles are in
the ratio 2:3, find the angles ?
2x+3x = 5x
5X = 180, so X = 36
thus the angles are 72 and 108 degree
respectively

11. 5 DECEMBER 09 www.afterschoool.tk 11
A person at a distance of 10 meters from a
tree finds angles of elevation of the top of
tree to be 45 degree, what is the height of
the tree
Tan = perpendicular /base
tan 45 = 1
thus height of tree is 10 meters. Answer

12. 5 DECEMBER 09 www.afterschoool.tk 12
60 meter tall tower has a shadow
of 60/sqrt(3) meters in lenght.
Find the elevation of Sun?
perpendicular/base = 60/60/sqrt(3) = sqrt(3)
thus it should be tan 60 degree. Answer

13. 5 DECEMBER 09 www.afterschoool.tk 13
400000 to be paid on monthly
instalments in 3 years, rate 15%,
payment in the beginning of the
month, find instalment
Present value=annuity/rate (1+rate)(1-
(1+rate)^-n
rate = 15/(12*100) = .0125
400000=a/.0125 * (1.0125)(1-(1.0125)^-36)
=13695 answer

14. 5 DECEMBER 09 www.afterschoool.tk 14
Rishi buys a TV in 48000 on
instalments. 8000Downpayment and
remaining in 15 instalments. Rate :
18%. find annual instalment
Present value=annuity/rate (1+rate)(1-
(1+rate)^-n
rate = 18/(100) = .18
40000=a/.18 * (1-(1.18)^-15)
= 7856 answer

15. 5 DECEMBER 09 www.afterschoool.tk 15
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