Geometric Themes for Class 8: Explained with Important Questions and Answers

Exploring Some Geometric Themes for Class 8 are available in this Maths article. Exploring Some Geometric Themes for Class 8 are very useful to solve the problems easily. This article helps the students to know the key questions and answers about Geometric Themes. Geometric themes cover patterns, shapes, solid figures, and visual ideas in geometry, which we use in everyday calculations. Our subject experts have provided detailed solutions for these problems based on the CBSE syllabus and the NCERT textbook. This material helps students revise the chapter easily and perform well in the final examination.

Table of Contents

• Exercise 1: Geometric Shapes and Properties Questions
• Exercise 2: Angles and Polygon Questions
• Exercise 3: Area and Perimeter Questions
• Exercise 4: Symmetry and Transformations Questions
• Exercise 5: Geometric Themes MCQ Questions
• Most Repeated Board Questions On Geometric Themes for Class 8

Exercise 1: Geometric Shapes and Properties Questions

Question 1: How many lines of symmetry does a square have?

Solution:

A square can be divided into equal halves in 4 different ways.

Answer: 4 lines of symmetry

Question 2: Find the sum of interior angles of a pentagon.

Solution:

Using the polygon angle sum formula:

(n−2)×180

For a pentagon:

(5−2)×180=540∘

Answer: 540°

Question 3: What is the measure of each exterior angle of a regular hexagon?

Solution

360∘6=60∘

Answer: 60°

Question 4: Find the perimeter of a rectangle whose length is 12 cm and breadth is 8 cm.

Solution

Perimeter of rectangle:

2(l+b)

Substitute values:

2(12+8)=40

Answer: 40 cm

Question 5: State whether a circle has any line of symmetry.

Solution

A circle can be divided into equal halves through any diameter.

Answer: A circle has infinitely many lines of symmetry.

Exercise 2: Angles and Polygon Questions

Question 1: Find the value of x if two complementary angles are x and 35°.

Solution

Complementary angles add up to 90°.

x+35∘=90∘

x=55∘

Answer: 55°

Question 2: Find the sum of interior angles of an octagon.

Solution

(8−2)×180=1080∘

Answer: 1080°

Question 3: Each exterior angle of a regular polygon is 45°. Find the number of sides.

Solution

360∘45∘=8

Answer: 8 sides

Question 4: What is the angle sum property of a triangle?

Solution

The sum of all interior angles of a triangle is:

180∘

Answer: 180°

Question 5: Two angles are supplementary. If one angle is 125°, find the other angle.

Solution

Supplementary angles add up to 180°.

180∘−125∘=55∘

Answer: 55°

Exercise 3: Area and Perimeter Questions

Question 1: Find the area of a square whose side is 9 cm.

Solution

Area of square:

a2

Substitute value:

92=81

Answer: 81 cm²

Question 2: Find the area of a rectangle of length 15 cm and breadth 6 cm.

Solution

15×6=90

Answer: 90 cm²

Question 3: Find the circumference of a circle of radius 7 cm.

Solution

Circumference formula:

2πr

Substitute values:

2×227×7=44

Answer: 44 cm

Question 4: Find the area of a triangle with base 10 cm and height 8 cm.

Solution

Area of triangle:

12×10×8=40

Answer: 40 cm²

Question 5: Find the perimeter of a square of side 14 cm.

Solution

Perimeter formula:

4×14=56

Answer: 56 cm

Exercise 4: Symmetry and Transformations Questions

Question 1: What is rotational symmetry?

Solution

A figure has rotational symmetry if it looks the same after rotation through a certain angle.

Answer: A shape matching itself after rotation has rotational symmetry.

Question 2: How many lines of symmetry does an equilateral triangle have?

Solution

Each vertex divides the triangle into two equal parts.

Answer: 3 lines of symmetry

Question 3: What is the order of rotational symmetry of a rectangle?

Solution

A rectangle matches itself twice during one full rotation.

Answer: Order = 2

Question 4: Name the transformation in which a figure slides without turning.

Solution

The movement is called translation.

Answer: Translation

Question 5: What is reflection symmetry?

Solution

If one half of a figure is the mirror image of the other half, it has reflection symmetry.

Answer: Mirror-image symmetry is called reflection symmetry.

Exercise 5: Geometric Themes MCQ Questions

Question 1: The sum of interior angles of a quadrilateral is:

A) 180°
B) 270°
C) 360°
D) 540°

Solution

(4−2)×180=360∘

Answer: C) 360°

Question 2: A regular polygon has all:

A) Unequal sides
B) Equal sides and equal angles
C) Equal sides only
D) Equal angles only

Answer: B) Equal sides and equal angles

Question 3: The area of a square with side 12 cm is:

A) 124 cm²
B) 132 cm²
C) 144 cm²
D) 156 cm²

Solution

122=144

Answer: C) 144 cm²

Question 4: A circle has:

A) One line of symmetry
B) Two lines of symmetry
C) Four lines of symmetry
D) Infinite lines of symmetry

Answer: D) Infinite lines of symmetry

Question 5: The exterior angle of a regular pentagon is:

A) 60°
B) 72°
C) 90°
D) 108°

Solution

360∘5=72∘

Answer: B) 72°

Most Repeated Board Questions On Geometric Themes for Class 8

Question 1: Find the sum of the interior angles of a hexagon.

Solution

Using the polygon angle sum formula:

(n−2)×180

For a hexagon:

(6−2)×180=720∘

Answer: 720°

Question 2: Each exterior angle of a regular polygon is 30°. Find the number of sides of the polygon.

Solution

Number of sides:

360∘30∘=12

Answer: 12 sides

Question 3: Find the area of a square whose side length is 15 cm.

Solution

Area of square:a2

Substitute the value:152=225

Answer: 225 cm²

Question 4: Find the perimeter of a rectangle whose length is 18 cm and breadth is 9 cm.

Solution

Perimeter formula:2(l+b)

Substitute values:2(18+9)=54

Answer: 54 cm

Question 5: The angles of a triangle are in the ratio 2:3:4. Find the angles.

Solution: Let the angles be:

2x,3x,4x

Using angle sum property:

2x+3x+4x=180∘

9x=180∘

x=20∘

Angles:

40∘,60∘,80∘

Answer:40°,60°,80°

Question 6: Find the circumference of a circle of radius 14 cm.

Solution

Circumference formula:2πr

Substitute values:

2×227×14=88

Answer: 88 cm

Question 7: How many lines of symmetry does a regular hexagon have?

Solution

A regular hexagon can be divided into equal halves in 6 ways.

Answer: 6 lines of symmetry

Question 8: Find the area of a triangle with base 12 cm and height 9 cm.

Solution

Area of triangle:

12×12×9=54

Answer: 54 cm²

Question 9: Two supplementary angles are in the ratio 5:7. Find the angles.

Solution

Let the angles be:

5x and 7x

Since supplementary angles add up to 180°:

5x+7x=180∘

12x=180∘

x=15∘

Angles: 75° and 105°

Answer: 75° and 105°

Question 10: Find the measure of each exterior angle of a regular octagon.

Solution

360∘8=45∘

Answer: 45°