+0  
 
0
51
1
avatar+156 

Please help. I don't understand this. Please show work. Thank you!

mathelp  Aug 22, 2018
 #1
avatar+88775 
+1

Top  left figure....we have  a hexagon....it it composed of 12 equal right triangles.....

each  has  legs  of  45/2  and 45 / [2√3] units.....each triangle has an area  of  (1/2) (product of the legs)...so we have

 

Area  =

12 * (1/2) * (45/2) * (45 / [2√3 ] =

6 * 45^2 / [4√3] =

2025√3 / 2 units^2  ≈

1753.7  units^2

 

The next three figures are  equilateral triangles.....their areas  =  [√3/4] * side^2

I'll calculate the area of the one with a side length of   20√3....you should be able to do the other two

Area  = [√3/4 ] [20√3]^2   =  [√3/ 4] [ 1200]  = 300√3  units^2 ≈ 519.6 units^2

 

The last two figures are also equilateral triangles  with circumradiuses  of 14 and 28...the area of either  is given by  3* (1/2)(circumradius)^2 * √3/2

The area of the  one with the circumradius of 14  =

3*(1/2) (14)^2 * √3/2  =

(3/4)(196)√3  =

147√3  units^2 ≈

254.6 units^2

 

You should be able to calculate the area of the one with the circumradius of 28 based on this

 

cool cool cool

CPhill  Aug 22, 2018

19 Online Users

avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.