Geometry Special Right Triangles help (ASAP)

1.  We have 12 congruent triangles here

We can find the base of each  as

cos 60  =  base/14    

 1/2  = base / 14      multiply both sides by 14

7  = base

We can find the height of each as

sin 60  =  a / 14     

√3/2  = a / 14    multiply both sides by 14

7√3  = a

So......the area of the hexagon is

12  * (1/2) (base)(height)  =

6 ( 7) (7√3)  =  294√3  cm^2

2.  For the lateral surface area, we have 8 congruent triangles  each with the same base as the height because both are opposite 45 degree angles

The base of each triangle  =  height  =  5

So....the lateral surface area  =

8 (1/2) (base) (height)  =

4 (5)(5)  =  100

The area of the base  is just  side^2  =  10^2   =  100

So.....the  surface area  =  100 + 100  =   200 ft^2

3.   We have 8 congruent 30-60-90 triangles

The base of each  =  4.6/ 2   =  2.3

The height of each is opposite the 60° angle  = √3 * base  = √3 * 2.3

So.....the lateral surface area  is

8 (1/2) (base) (height) =

4 (2.3)(√3 * 2.3)  ≈  36.65 yd^2 

The base area  =  side^2  =  4.6^2  = 21.16 yd^2

So....the total area  is     36.65 + 21.16  =  57.8 yd^2

Last one

We have 8 congruent triangles each with a base  of 5.8 cm

We can use the Pythagorean Theorem to find the slant height of each  =

√[ 7^2 + 7^2]  =  √ [2 * 7^2]   =  7√2

So.....the lateral area  is

8 (1/2) (base) (slant height)  =

4 (5.8) (7√2 )  =  229. 7 cm^2