Therefore, the lengths are the sides of a triangle because the sum of lengths of two sides must be greater than the third side. All the sum of length of 2 sides are greater than the third side.

5 0

3 years ago

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What is the number of diagonals that intersect at a given vertex of a hexagon, heptagon, 30-gon and n-gon?

DENIUS [597]

Answer:

i. 9

ii. 14

iii. 405

iv. $\frac{n(n-3)}{2}$

Step-by-step explanation:

The number of diagonals in a polygon of n sides can be determined by:

$\frac{n(n-3)}{2}$

where n is the number of its sides.

i. For a hexagon which has 6 sides,

number of diagonals = $\frac{6(6-3)}{2}$

= $\frac{18}{2}$

= 9

The number of diagonals in a hexagon is 9.

ii. For a heptagon which has 7 sides,

number of diagonals = $\frac{7(7-3)}{2}$

= $\frac{28}{2}$

= 14

The number of diagonals in a heptagon is 14.

iii. For a 30-gon;

number of diagonals = $\frac{30(30-3)}{2}$

= $\frac{810}{2}$

= 405

The number of diagonals in a 30-gon is 405.

iv. For a n-gon,

number of diagonals = $\frac{n(n-3)}{2}$

The number of diagonals in a n-gon is $\frac{n(n-3)}{2}$

7 0

3 years ago

The dimensions of a trapezoid are shown below. Which equation could you use to find the Area of the Trapezoid?

Contact [7]

Answer:

See Explanation

Step-by-step explanation:

No trapezoid is attached; so, I will solve on a general note

The area of a trapezoid is:

$Area = \frac{1}{2}(Sum\ of\ parallel\ sides) * Height$

Using the attached image as a point of reference;

The parallel sides are: AD (6cm) and BD (12cm)

The height is 4cm

So, the area is:

$Area = \frac{1}{2} * (6cm + 12cm) * 4cm$

$Area = 18cm * 2cm$

$Area = 36cm^2$

7 0

3 years ago

Emilio by 5.65 pounds of green grapes and 3.07 pounds of red grapes. He divided the grapes equally into 14 bags, each bag of gra

Mazyrski [523]

Answer:

5.65+3.07=8.72

8.72/16=0.545

Each bag of gapes weight 0.545 pounds.

Step-by-step explanation:

8 0

3 years ago

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