Pentagon question

Hey everyone. I have another question.

The area of a regular pentagon is 150cm^2. Calculate the length of one side of the pentagon

Thanks

Reply 1

*Examboy*

A pentagon forms three triangles.

Each triangle therefore has an area of 50cm^2.

Area of triangle = 1/2 x a x b x sin C.

Therefore it is solvable from there...

Reply 2

Umairy363

*Examboy*

A pentagon forms three triangles.

Each triangle therefore has an area of 50cm^2.

Area of triangle = 1/2 x base x height.

Therefore it is solvable from there...

The triangles formed are not right angle :s-smilie:

therefore the half base times height does not work. The question is more about the formula 0.5abSinC

Reply 3

Corsix

A pentagon can be constructed from 3 triangles, but they will not be identical triangles. Try 5 triangles, which makes them 5 identical triangles, each with area 30 cm^2.

Reply 4

*Examboy*

Umairy363

The triangles formed are not right angle :s-smilie:

therefore the half base times height does not work. The question is more about the formula 0.5abSinC

Sorry.

1/2 x a x b x Sin C = 50

Find sin C and then using that, a and b are equal so it is possible to solve it.

Reply 5

1721

Umairy363

The triangles formed are not right angle :s-smilie:

therefore the half base times height does not work. The question is more about the formula 0.5abSinC

make it 10 right angled triangles then,
wit a line from the middle to every point and every mid point of the edge

Reply 6

Umairy363

Corsix

A pentagon can be constructed from 3 triangles, but they will not be identical triangles. Try 5 triangles, which makes them 5 identical triangles, each with area 30 cm^2.

ive tried that. Assuming the the apex of the triangle is 72 degrees (360 degrees divided by 5) therefore the triangles arent equilateral but are equally with respect to each other, have i got that right so far?

Reply 7

Umairy363

They are actually isoceles triangles, therefore the actual base had to be worked out. Thanks ive worked it out. Thankyou everyone for your help

Reply 8

Corsix

Yes, the triangles will be isosceles, with the 'apex' being 72 degrees, and the two sides adjacent to the apex having the same length (which is different to the side length of the polygon). Use

Area=0.5ab\sin(C)=30

with

a=b

to find the lengths of these two identical sides. Then a method of your choice to find the length of the remaining side (I'd recommend the sine rule).