#1**+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

CPhill Aug 22, 2018