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# Help

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Aug 22, 2018

#1
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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

Aug 22, 2018