Thread: Trigonometry and area

I need help with a few problems.

I need help finding the area of a regular hexagon with an apothem of 19mm.
Also I need help with finding the area of a octagon with a radius of 20in.

Can someone also double check if I did these ratio right?

A similar pair of triangles the small triangle has a area of 12 cm and the large has an area of 48 cm.
Ratio of areas = 1:4
Scale factor = 4
Ratio of perimeter = 1:4

Did I do that one right?
Thanks for your help.

Originally Posted by Jubbly

I need help with a few problems.

I need help finding the area of a regular hexagon with an apothem of 19mm.
Also I need help with finding the area of a octagon with a radius of 20in.

Can someone also double check if I did these ratio right?

A similar pair of triangles the small triangle has a area of 12 cm and the large has an area of 48 cm.
Ratio of areas = 1:4
Scale factor = 4 in terms of two-dimensional areas
Ratio of perimeter = 1:4 perimeter is one-dimensional

Did I do that one right?
Thanks for your help.

Hi Jubbly,

As area is 0.5(base)(height)

Quadrupled area corresponds to 0.5[(2)base][2(height] for similar triangles.

Therefore the ratio of perimeters, corresponding to area ratio of 1:4, is 1:2

see the attached sketch.