CBSE Class 6 Mathematics Understanding Elementary Shapes Worksheet Set 03

I) Fill in the blanks :

Question 1. An angle whose measure is greater than that of a right angle is _______________________
Answer: Obtuse angle
In simple words: An angle between \(90^\circ\) and \(180^\circ\) is an obtuse angle.

Exam Tip: Remember that a right angle is exactly \(90^\circ\).

Question 2. Three edges meet at a point called a ________________________.
Answer: Vertex
In simple words: The corner point where edges of a 3D shape meet is called a vertex.

Exam Tip: For a 3D solid, vertices are the corner points.

Question 3. A ___________________________ is larger than a straight angles.
Answer: Reflex angle
In simple words: An angle measuring greater than \(180^\circ\) and less than \(360^\circ\) is a reflex angle.

Question 4. A Polygon with 5 sides is called a ___________________________.
Answer: Pentagon
In simple words: A five-sided closed polygon is known as a pentagon.

Exam Tip: Penta means five.

Question 5. A triangle having all three unequal sides is called a ____________________.
Answer: Scalene triangle
In simple words: A triangle with no sides equal in length is a scalene triangle.

Exam Tip: Scalene means all sides have different lengths.

II) Write down the measure of

Question 1(a). Some acute angles.
Answer: \(30^\circ, 45^\circ, 60^\circ, 75^\circ\)
In simple words: Acute angles measure less than \(90^\circ\).

Exam Tip: Any angle strictly between \(0^\circ\) and \(90^\circ\) is acute.

Question 1(b). Some obtuse angles.
Answer: \(95^\circ, 120^\circ, 135^\circ, 150^\circ\)
In simple words: Obtuse angles measure greater than \(90^\circ\) and less than \(180^\circ\).

Exam Tip: Do not confuse obtuse angles with reflex angles.

Question 1(c). What is the measure of a straight angle?
Answer: \(180^\circ\)
In simple words: A straight line forms an angle of \(180^\circ\).

Exam Tip: Equivalent to two right angles (\(2 \times 90^\circ\)).

III) What shape is

Question 1(a). A brick.
Answer: Cuboid
In simple words: A brick has rectangular faces of different dimensions, making it a cuboid.

Exam Tip: 3D shapes with rectangular faces are cuboids.

Question 1(b). A match box
Answer: Cuboid
In simple words: A match box has the shape of a rectangular prism, which is a cuboid.

Exam Tip: Similar to a brick shape.

Question 1(c). A sweet laddu
Answer: Sphere
In simple words: A round sweet laddu resembles a ball, which is a sphere.

Exam Tip: Perfectly round 3D objects are spheres.

Question 1(d). A ball
Answer: Sphere
In simple words: A ball is a round 3D geometrical shape called a sphere.

Exam Tip: Think of a globe or a football.

Question 1(e). A die
Answer: Cube
In simple words: A playing die has 6 equal square faces, forming a cube.

Exam Tip: All edges of a cube are equal in length.

Question 1(f). A road roller
Answer: Cylinder
In simple words: The heavy rolling drum of a road roller is cylindrical in shape.

Exam Tip: A cylinder has two circular bases and a curved surface.

IV) Name the types of following triangles :

Question 1. \(\Delta LMN\) with \(m \angle L = 80^\circ\), \(m \angle M = 70^\circ\), \(m \angle N = 30^\circ\).
Answer: Acute-angled triangle
In simple words: Since all three angles are less than \(90^\circ\), it is an acute-angled triangle.

Exam Tip: Check if every interior angle is strictly less than \(90^\circ\).

Question 2. \(\Delta ABC\) with \(m \angle A = 90^\circ\).
Answer: Right-angled triangle
In simple words: A triangle with one right angle (\(90^\circ\)) is a right-angled triangle.

Exam Tip: Look for the square corner symbol or \(90^\circ\) measure.

Question 3. \(\Delta PQR\) such that \(PQ = QR = PR = 8\text{ cm}\).
Answer: Equilateral triangle
In simple words: A triangle with all three sides equal is an equilateral triangle.

Exam Tip: Equal sides also mean equal angles (\(60^\circ\) each).

Question 4. \(\Delta XYZ\) with \(AB = 8\text{ cm}\), \(BC = 5\text{ cm}\), \(CA = 5\text{ cm}\) (Note: referring to triangle side lengths).
Answer: Isosceles triangle
In simple words: Since two sides are equal (\(5\text{ cm}\) and \(5\text{ cm}\)), it is an isosceles triangle.

Question 5. Triangle with lengths of sides \(7\text{ cm}\), \(8\text{ cm}\) and \(9\text{ cm}\).
Answer: Scalene triangle
In simple words: All three side lengths are different, so it is a scalene triangle.

Exam Tip: Different side lengths correspond to scalene classification.

Question 6. \(\Delta PQR\) with \(m \angle Q = 90^\circ\) and \(PQ = QR\).
Answer: Isosceles right-angled triangle
In simple words: It has one \(90^\circ\) angle (right-angled) and two equal sides (isosceles).

Exam Tip: Combining conditions gives a compound name.

Question V. Let \(\overline{PQ}\) be the perpendicular to the line segment \(\overline{XY}\). Let \(\overline{PQ}\) and \(\overline{XY}\) intersect in the point A. What is the measure of \(\angle PAY\)?
Answer: \(90^\circ\)
In simple words: Since the line segments are perpendicular, they meet at a right angle of \(90^\circ\).

Exam Tip: Perpendicular lines always intersect at \(90^\circ\).

VI) Classify each one of the following angles as right, straight, acute, obtuse or reflex.

Question a.
Answer: Obtuse angle
In simple words: The angle shown is greater than \(90^\circ\) and less than \(180^\circ\).

Exam Tip: Visually wider than a right angle.

Question b.
Answer: Acute angle
In simple words: The angle is narrower than a right angle, measuring less than \(90^\circ\).

Exam Tip: Sharp corner smaller than \(90^\circ\).

Question c.
Answer: Reflex angle
In simple words: The arc covers an angle greater than \(180^\circ\).

Exam Tip: The reflex indicator curves around the outside of the vertex.

Question d.
Answer: Acute angle
In simple words: The interior angle formed is less than \(90^\circ\).

Exam Tip: Check the angle arc inside the peak.

Question e.
Answer: Right angle
In simple words: The arms meet perpendicular to form a \(90^\circ\) corner.

Exam Tip: Forms an L-shape.

Question f.
Answer: Acute angle
In simple words: The angle is less than \(90^\circ\).

Exam Tip: Narrow opening.

VII) Find the angle measure between the hands of the clock in each figure

Question a. Clock showing 3 o'clock.
Answer: Right angle (\(90^\circ\))
In simple words: At 3 o'clock, the minute hand is at 12 and the hour hand is at 3, forming a quarter turn.

Exam Tip: Each hour mark on a clock represents \(30^\circ\) (\(3 \times 30^\circ = 90^\circ\)).

Question b. Clock showing acute angle position between hands.
Answer: Acute angle
In simple words: The angle between the hands is less than \(90^\circ\).

Exam Tip: Count the hour spaces to verify the angle.

Question c. Clock showing 6 o'clock.
Answer: Straight angle (\(180^\circ\))
In simple words: At 6 o'clock, the hands point in opposite directions, forming a straight line.

Exam Tip: Half-turn rotation equals \(180^\circ\).

VIII) Name each polygon

Question a. 5-sided polygon
Answer: Pentagon
In simple words: A closed 2D shape with 5 straight sides is a pentagon.

Exam Tip: Count the number of straight sides carefully.

Question b. 3-sided polygon
Answer: Triangle
In simple words: A polygon with 3 sides is a triangle.

Exam Tip: The simplest polygon is a triangle.

Question c. 4-sided polygon (rhombus/quadrilateral)
Answer: Quadrilateral
In simple words: Any 4-sided closed figure is a quadrilateral.

Exam Tip: Quad means four.

Question d. 8-sided polygon
Answer: Octagon
In simple words: A polygon with 8 sides is an octagon.

Exam Tip: Octa refers to eight (like an octopus).

Question e. 5-sided irregular polygon
Answer: Pentagon
In simple words: Even if irregular, a 5-sided polygon is a pentagon.

Exam Tip: Classification depends on the number of sides, not regularity.

IX) Fill in the blanks regarding 3D shapes:

Question 1. A cuboid has ______________________ faces.
Answer: 6 faces
In simple words: A cuboid has 6 flat rectangular faces.

Exam Tip: Think of a room with floor, ceiling, and 4 walls.

Question 2. Each face has ______________________ edges. (Referring to face boundaries or standard textbook properties)
Answer: 4 edges
In simple words: Each rectangular face of a cuboid is bounded by 4 edges.

Exam Tip: A rectangle has 4 sides.

Question 3. Each face has _________________ vertices.
Answer: 4 vertices
In simple words: Each flat rectangular face has 4 corner vertices.

Exam Tip: Corners of a face correspond to vertices.