Analyze the diagram below and complete the instructions that follow.
/
find the surface area of the composite solid if the base is a regular hexagon. round your answer to the nearest hundredth.
a.
471.53 m2
b.
615.53 m2
c.
709.06 m2
d.
802.59 m2

According to the image:
the right hexagonal pyramid surface area is given by the following formula:

S = 3√3 / 2) a² + 3a √h²+3a²/4
a = the base edge
h = the height of the pyramid

looking at the image  a =6m,  h =21m - 7m= 14m

so the surface area is S = 3√3 / 2) 6² + 3*6√14²+3*6²/4 =93.53+ 14.93=108.46 m²

for the another one
the figure is a prism hexagonal
its surface area is 
SA= 6ah +3√3 a²
a= base edge, h =height
in our case a =6m and h = 7m
so SA= 6*6*7 + 3√3 * 6²= 252 + 187 = 439 m²

finally, the surface area of the complete image is 
ST= S + SA = 108.46 m² + 439 m² = 547.52 m²
it is so approximate
 to B. 615.53 m2
look at the image

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.