First one :
The slant height, h, is given by :
sin 60 = h / 8 multiply both sides by 8
8 * sin 60 = h
8 * √3 / 2 = h
4√3 m = h
Second one
The base area is composed of 6 equilateral triangles.......
The total area is given by : 6 (1/2) (14) (14) sin (60°) = 3 * 196 * √3/ 2 = 294√3 cm^2
Third one ;
The base area is a square with a side of 6 ft....so its area = 6^2 = 36 ft^2
The sides are triangles with bases of 6 and heights of 3....and we have 4 of them....so their area is just :
4 * (1/2) (6) * 3 = 36 ft^2
So the surface area = [ 36 + 36 ] ft^2 = 72 ft^2
Fourth one :
The base is a square with a side of 6.2 yd....so its area is (6.2)^2 = 38.44 yd^2
The sides are 4 equal area triangles.....their bases are 6.2 yds
Their heights, h, can be found as tan(60) = h / (6.2 * (1/2) )
√3 = h / 3.1 multiply both sides by 3.1
3.1 * √3 = h
So the area of each triangle = (1/2) base) (height) = (1/2) (6.2) * 3.1 * √3 ≈ 16.645 yd^2
And we need to multiply ths by 4 = 66.58 yd^2
So...the total surface area is [ 38.44 + 66.58 ] yds^2 ≈ 105 yds^2
Last one ;
We have 8 equal area triangles comprising the lateral surface area .......we can find the height of each triangle as the hypotenuse of a right triangle with legs of 8.......this height is : √ [ 8^2 + 8^2 ] = 8√2 cm
So....the total lateral surface area is
8 * (1/2) base of each triangle * its height =
8 * (1/2) * 6.6 * 8√2 =
4 * 6.6 * 8√2 = 298.7 cm^2
