This set of Aptitude Questions and Answers (MCQs) focuses on “Polygons”.

1. Which of the following options does not describes the interior angles of a convex polygon correctly?

a) Obtuse angle

b) Acute angle

c) Reflex angle

d) Right angle

View Answer

Explanation: A polygon is called a convex polygon if all the interior angles are less than 180°. This means that the angle can be acute, right and obtuse. Thus, reflex angle is the wrong option.

2. How many sides does a polygon having sum of interior angles as 2340 will have?

a) 15

b) 16

c) 13

d) 12

View Answer

Explanation: Given,

Sum of interior angles = 2340

Let the number of sides be n.

➩ 2340 = (n – 2) * 180

➩ 2340 = 180n – 360

➩ 2340 + 360 = 180n

➩ 2700 = 180n

➩ 2700 / 180 = n

➩ n = 15

3. Which of the following is the correct option with respect to the area of a regular pentagon of side z?

a) 1 / 5 * (5(5 + 2√5))^{1/2} * z^{2}

b) \(\frac {1}{4}\) (5(5 + 2√5))^{1/2} * z^{2}

c) \(\frac {1}{4}\) (5 + 2√5)^{1/2} * z^{2}

d) \(\frac {1}{4}\) (25(5 + 2√5))^{1/2} * z^{5}

View Answer

Explanation: Given,

Side of regular pentagon = z.

Correct formula for area of a regular pentagon = \(\frac {1}{4}\) (5(5 + 2√5))

^{1/2}* z

^{2}.

4. What will be the measure of each interior angle of a regular hexagon in degrees?

a) 120

b) 140

c) 80

d) 60

View Answer

Explanation: As we know,

Sum of interior angles of polygon of side n = (n – 2) * 180

For a regular hexagon n = 6

Sum of interior angles = (6 – 2) * 180

= 4 * 180

= 720.

Now the hexagon will have 6 equal interior angles thus,

Each interior angle = 720 / 6

= 120 degrees

5. Which of the following options represents the correct expression for calculating the area of a regular hexagon of side a?

a) (3√3 / 2) * a^{3}

b) (6√3 / 2) * a^{2}

c) (3√3 / 2) * a^{2}

d) (3√9 / 2) * a^{3}

View Answer

Explanation: Given,

The side of regular hexagon = a

Correct formula for area of regular hexagon = (3√3 / 2) * a

^{2}.

6. If the base of a rhombus is 8 cm and its altitude is 5 cm the, what will be the area (in sq. cm) of this rhombus?

a) 60

b) 30

c) 20

d) 40

View Answer

Explanation: Given,

l = 8 cm, h = 5 cm

Area of rhombus = l * h

= 8 * 5

= 40 cm

^{2}

7. A four sided polygon PQRS is such that it is formed of two equilateral triangles PQS and QRS joined together. The area of a PQRS is 8√3 cm^{2}, then what will be the perimeter (in cm) of PQRS?

a) 16

b) 32

c) 12

d) 20

View Answer

Explanation: Given,

Area of PQRS = 8√3 cm

^{2}= 2 * Area of PQS = 2 * Area of QRS

Let the length of side of PQRS = x cm

Area of PQS = √3 / 4 * x

^{2}

On equating

➩ 2 * √3 / 4 * x

^{2}= 8√3

➩ √3 / 4 * x

^{2}= 4√3

➩ x

^{2}= 4√3 * 4 / √3

➩ x

^{2}= 16 cm

^{2}

➩ x = 4 cm.

Perimeter of PQRS = 4 * x

= 4 * 4 cm

= 16 cm

8. By what percentage is the area of a regular pentagon increased if its side is doubled?

a) 600%

b) 500%

c) 300%

d) 400%

View Answer

Explanation: Let the original length = x

Original area = \(\frac {1}{4}\) (5(5 + 2√5))

^{1/2}* x

^{2}

New length = 2x

New area = \(\frac {1}{4}\) (5(5 + 2√5))

^{1/2}* (2x)

^{2}

= \(\frac {1}{4}\) (5(5 + 2√5))

^{1/2}* 4x

^{2}

% increase in area = difference in area / original area * 100

= 300%.

9. What will be the area (in sq. cm) of an equilateral triangle of side 1 cm?

a) √3 / 2

b) √3 / 4

c) √3 / 8

d) 3√3 / 4

View Answer

Explanation: Given,

a = 1cm

Area = √3 / 4 * a

^{2}

= √3 / 4 * (1)

^{2}

= √3 / 4 cm

^{2}

10. What will be the area (in sq. m) of a hexagonal field having side as 2m?

a) 6√3

b) 3√3

c) 3√3 / 2

d) 3√3 / 4

View Answer

Explanation: Given,

a = 2m

Area = 3√3 / 2 * a

^{2}

= 3√3 / 2 * (2)

^{2}

= 3√3 / 2 * 4

= 6√3 m

^{2}

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