How many diagonals can be drawn by joining the vertices of an octagon?
- A20Correct
- B24
- C28
- D64
Explanation
To find the number of diagonals in a polygon, we use the formula: n times (n minus 3) divided by 2, where n is the number of sides.
An octagon has 8 sides, so n equals 8.
Plugging this into the formula: 8 times (8 minus 3) divided by 2 8 times 5 divided by 2 40 divided by 2 20
Alternatively, you can think of it this way: From 8 vertices, you can choose 2 to form a line in 28 ways (8 times 7 divided by 2). Out of these 28 lines, 8 are the sides of the octagon. Subtracting the 8 sides from the total lines (28 minus 8) leaves 20 diagonals.
Therefore, the correct answer is 20.
Related questions
More UPSC Prelims practice from the same subject and topic.
- Prelims 2018CSATQuantitative Aptitude
A solid cube of 3 cm side, painted on all its faces, is cut up into small cubes of 1 cm side. How many of the small cubes will have exactly two painted faces?
- Prelims 2018CSATQuantitative Aptitude
Twelve equal squares are placed to fit in a rectangle of diagonal 5 cm. There are three rows containing four squares each. No gaps are left between adjacent squares. What is the area of each square?
- Prelims 2018CSATQuantitative Aptitude
Consider the following sum: • +1• +2• +• 3 + • 1 = 21• In the above sum, • stands for
- Prelims 2018CSATQuantitative Aptitude
A train 200 metres long is moving at the rate of 40 kmph. In how many seconds will it cross a man standing near the railway line?
- Prelims 2018CSATQuantitative Aptitude
If X is between -3 and -1, and Y is between -1 and 1, then X ² - Y² is in between which of the following?
- Prelims 2018CSATQuantitative Aptitude
X and Y are natural numbers other than 1, and Y is greater than X. Which of the following represents the largest number?