Find the surface area of each prism. round to the nearest tenth if necessary while doing your calculations as well as in your final answer.
question 14 options:
340 units2
241 units2
262 units2
301 units2

340 units2

Step-by-step explanation:

draw perpendicular line from upper left corner of trapezoid to cut bottom line(=9) into two part having length 3 and 6. Now a triangle and rectangle are formed.

The triangle has base=3, angle 60 degrees and angle of 90 degrees.

Finding third angle:

180-60-90= 30

finding other two sides of triangle by using law of sines:

a/sinA=b/sinB

3/sin30=b/sin60

b=3sin60/sin30

b=3(0.866)/0.5

b=5.2

b is the perpendicular line we drew

a/sinA=b/sinB

3/sin30=c/sin90

c=3sin90/sin30

c=3(1)/0.5

c=6

c is the hypotenuse of the triangle

Now Finding the perimeter of base:

The perimeter of the base=sum of the lengths of sides.

p=6+9+6+5.2

 =26.2

area of trapezoid:

A= (a+b)h/2

  = (6+9)(5.2)/2

  =39

total surface area of prism:

TSA= ph + 2A

where h is height of prism = 10

TSA= 26.2(10) + 2(39)

       =340

Hence total surface area of the given prism is 340 units square!

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it