Question

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

Answer 1

340 units2 is the correct answer.

Explanation:

Answer 2

340 units2

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!