# Mathematics Questions and Answers – Properties of Polygons-1

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This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Properties of Polygons-1”.

1. What will be the sum of internal angles of a septagon?
a) 650
b) 700
c) 450
d) 900

Explanation: The sum of the interior angles of a polygon can be calculated using the formula = (number of sides – 2) × 180
Here, number of sides is 7.
So, the sum of interior angles of a septagon = (7 – 2) × 180 = 5 × 180 = 900

2. What parameter is used to find the area and perimeter of a polygon?
a) Curve
b) Size
c) Length
d) Angle

Explanation: The length of the polygon can be used to find the perimeter and area of a polygon. Since, the perimeter and area are in relation with the sides of the polygon, therefore they play a major role in finding the two parameters.

3. What will be the area of the given figure if the length of one side is 10 cm and the height of the parallelogram is 15 cm? a) 225 cm2
b) 1225 cm2
c) 150 cm2
d) 75 cm2

Explanation: The given figure can be divided into two triangles. The total area of the parallelogram will be the sum of the areas of two triangles. Area of triangle = $$\frac{1}{2}$$ × base × height = $$\frac{1}{2}$$ × 10 × 15 = 75 cm2
Area of the parallelogram = 2 × area of triangle = 2 × 75 = 150 cm2
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4. A polygon is 3D shape with straight sides.
a) True
b) False

Explanation: A polygon is a shape constructed using straight sides. It is encompassed within the boundaries of lines in a regular or irregular manner. But a circle or any other curve does not fall under polygon. It is two dimensional in nature.

5. What will be the exterior angles of a hexagon?
a) 7.2°
b) 60°
c) 54°
d) 108°

Explanation: The exterior angles of a polygon can be found using the formula = $$\frac{360}{number \, of \,sides}$$.
Since, the number of sides of a hexagon is 6.
Therefore, the exterior angle of a hexagon is = $$\frac{360}{6}$$ = 60°

6. What is the circle which connects all the vertices of a polygon called?
a) Semi-circle
b) Incircle
c) Outer circle
d) Circumcircle

Explanation: A circle which connects all the vertices of the triangle is called as a circumcircle. Whereas, if touches the sides of the polygon internally then it is called as incircle.

7. What is a polygon with 50 sides called as?
a) Pentahexagon
b) Pentagon
c) Pentacontagon
d) Pentacontagion

Explanation: A polygon with fifty sides is called as pentacontagon. The sum of the interior angles of a pentacontagon is 8640° and the exterior angle of a pentacontagon is 7.2°.

8. What will be the sum of exterior angle of a regular polygon?
a) 360°
b) 180°
c) 540°
d) 120°

Explanation: The sum of the external angles of a regular polygon is always 360°. When we push all the angles of a convex polygon the angle converges and form a total of 360°. This angle is also called as perigon angle.

9. The circle inscribed inside a polygon is called a circumcircle.
a) False
b) True

Explanation: A circle inscribed in a polygon is called an incircle (in meaning inside). A circle circumscribing the polygon, or just touching the vertices of the polygon is called as circumcircle. 10. The radius of the incircle is the apothem of the polygon.
a) True
b) False

Explanation: An apothem is a line from the center of the regular polygon at right angles to any of its sides. This line is also the radius of the incircle. Hence, an apothem is the radius of the incircle of a regular polygon. In the given figure, the line AB is the apothem of the polygon as well as the radius of the incircle. Sanfoundry Global Education & Learning Series – Mathematics – Class 8.

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