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How many diagonals does each of the following have?

(a) A convex quadrilateral

(b) A regular hexagon

(c) A triangle.

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(a) 9 . (b) 2 . (c) 0

(a) 5 . (b) 4 . (c) 6

(a) 2 . (b) 0 . (c) 9

(a) 2 . (b) 9 . (c) 0 .

answer is D.

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Detailed Solution

Concept- General formula for no. The diagonal is (n-3) multiplied by no. of each vertex and then divided by 2.
Question Image

Formula is

d = (\frac{n (n - 3)}{2})

(a)A convex quadrilateral
As we know that in a convex quadrilateral there are four sides .
Therefore,

n = 4

Then, number of diagonal in convex quadrilateral is

d = \frac{n (n - 3)}{2}

d = \frac{4 (4 - 3)}{2}

d = \frac{4}{2}

d = 2

(b)A regular hexagon
As we know that in regular hexagon there is six sides
Therefore,

n = 6

Then, number of diagonal in regular hexagon is

d = \frac{n (n - 3)}{2}

d = \frac{6 (6 - 3)}{2}

d = \frac{18}{2}

d = 9

(c)A triangle
As we know that in a triangle there is three sides
Therefore,

n = 3

Then, number of diagonal in a triangle is

d = \frac{n (n - 3)}{2}

d = \frac{3 (3 - 3)}{2}

d = 0

Hence, the correct option is 4.

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