Q1: Which of the following is a polygon? (a) Circle (b) Rectangle (c) Oval (d) Curved line
Solution:
Ans: (b) Explanation: A polygon is a closed plane figure made up of straight line segments. A rectangle has four straight sides and is a polygon. A circle and oval have curved sides, so they are not polygons. A curved line is not a closed figure.
Q2: How many sides does a hexagon have? (a) 5 (b) 6 (c) 7 (d) 8
Solution:
Ans: (b) Explanation: A hexagon is a polygon with exactly 6 sides. The prefix "hex" means six. A pentagon has 5 sides, a heptagon has 7 sides, and an octagon has 8 sides.
Q3: Which shape has all sides equal and all angles equal? (a) Rectangle (b) Rhombus (c) Square (d) Trapezoid
Solution:
Ans: (c) Explanation: A square has all four sides equal in length and all four angles equal (each measuring 90 degrees). A rectangle has all angles equal but not all sides equal. A rhombus has all sides equal but not all angles equal. A trapezoid has neither all sides nor all angles equal.
Q4: What is the name of a triangle with no equal sides? (a) Equilateral triangle (b) Isosceles triangle (c) Scalene triangle (d) Right triangle
Solution:
Ans: (c) Explanation: A scalene triangle has no equal sides and no equal angles. An equilateral triangle has all three sides equal. An isosceles triangle has two equal sides. A right triangle is classified by its angle (one 90-degree angle), not by its sides.
Q5: Which quadrilateral has exactly one pair of parallel sides? (a) Parallelogram (b) Rectangle (c) Trapezoid (d) Rhombus
Solution:
Ans: (c) Explanation: A trapezoid has exactly one pair of parallel sides. A parallelogram, rectangle, and rhombus all have two pairs of parallel sides.
Q6: How many vertices does a pentagon have? (a) 4 (b) 5 (c) 6 (d) 7
Solution:
Ans: (b) Explanation: A pentagon is a polygon with 5 sides and therefore has 5 vertices (corner points). The number of vertices in a polygon is always equal to the number of sides.
Q7: Which of these is NOT a quadrilateral? (a) Square (b) Triangle (c) Trapezoid (d) Parallelogram
Solution:
Ans: (b) Explanation: A quadrilateral is a polygon with exactly 4 sides. A triangle has only 3 sides, so it is not a quadrilateral. Squares, trapezoids, and parallelograms all have 4 sides and are quadrilaterals.
Q8: What do we call a closed figure with 8 sides? (a) Hexagon (b) Heptagon (c) Octagon (d) Nonagon
Solution:
Ans: (c) Explanation: An octagon is a polygon with 8 sides. The prefix "octa" means eight. A hexagon has 6 sides, a heptagon has 7 sides, and a nonagon has 9 sides.
Section B: Fill in the Blanks
Q9: A polygon is a closed plane figure made up of straight __________ segments.
Solution:
Ans: line Explanation: A polygon must have straight line segments as its sides. Figures with curved sides, like circles, are not polygons.
Q10: A triangle with all three sides equal is called an __________ triangle.
Solution:
Ans: equilateral Explanation: An equilateral triangle has all three sides equal in length and all three angles equal (each measuring 60 degrees).
Q11: A quadrilateral with opposite sides parallel and all sides equal is called a __________.
Solution:
Ans: rhombus Explanation: A rhombus is a special quadrilateral where all four sides are equal in length and opposite sides are parallel. It can also be called a diamond shape.
Q12: The point where two sides of a polygon meet is called a __________.
Solution:
Ans: vertex Explanation: A vertex (plural: vertices) is the corner point where two sides of a polygon meet. Every polygon has the same number of vertices as it has sides.
Q13: A polygon with 10 sides is called a __________.
Solution:
Ans: decagon Explanation: A decagon is a polygon with exactly 10 sides. The prefix "deca" means ten.
Q14: A rectangle has __________ right angles.
Solution:
Ans: four (or 4) Explanation: A rectangle is a quadrilateral with four right angles (each measuring 90 degrees). This is one of the defining properties of a rectangle.
Section C: Word Problems
Q15: Sarah drew a triangle where two sides measure 5 inches each and the third side measures 3 inches. What type of triangle did Sarah draw?
Solution:
Ans: Final Answer: Isosceles triangle
Q16: A stop sign is shaped like a regular octagon. If each side of the stop sign measures 12 inches, what is the total distance around the stop sign (perimeter)?
Solution:
Ans: Step 1: An octagon has 8 sides. Step 2: Perimeter = \(8 \times 12 = 96\) inches Final Answer: 96 inches
Q17: Marcus is building a fence around his rectangular garden. The length of the garden is 15 feet and the width is 8 feet. How many feet of fencing does Marcus need?
Q18: A square has a perimeter of 36 centimeters. What is the length of one side of the square?
Solution:
Ans: Step 1: A square has 4 equal sides. Step 2: Length of one side = \(36 \div 4 = 9\) centimeters Final Answer: 9 centimeters
Q19: Emily is making a pentagon-shaped poster for her science project. If she needs to put a border around all 5 sides and each side measures 10 inches, how much border material does she need in total?
Solution:
Ans: Step 1: A pentagon has 5 sides. Step 2: Total border needed = \(5 \times 10 = 50\) inches Final Answer: 50 inches
Q20: A parallelogram has one side that measures 14 meters and another side that measures 9 meters. What is the perimeter of the parallelogram?
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