Question

Whats the surface area?

Answer 1

384 cm^2

Explanation:

First, find the area of rectangular prism, there are 6 sides, find three of the sides and double each of those sides and add them up:

Front/back:

4(15) = 60, double it: 60(2) = 120

Right/left:

The right side is inside- meaning it's included in the volume not the surface area, so don't double it:

6(4) = 24

Bottom/top:

6(15) = 90, double it: 90(2) = 180

Add the sides up:

120 + 24 + 180

= 324

Now find the SA of the right triangular prism:

Formula for area of triangle, A = BH(1/2)

Where "B" represents base and "H" represents height.

Find area of front and back:

(3)(4)(1/2) = 6, double it: 6(2) = 12

Now the bottom:

3(6) = 18

Slant:

5(6) = 30

Add them up:

12 + 18 + 30

= 60

Add total surface area:

324 + 60

= 384 cm^2

Answer 2

384 cm²

Explanation:

You want the surface area of the trapezoidal prism shown.

Surface area

The surface area of the prism is the sum of the area of the two trapezoidal bases and the area of the four rectangular faces. The formula can be written ...

SA = 2B +Ph

where B is the trapezoid area:

B = 1/2(b1 +b2)H . . . . . H is the height of the trapezoid, 4 cm

Base area

Filling in numbers, we have ...

B = 1/2(15 +3 +15)(4) = 66 . . . . cm²

Perimeter

The perimeter of the trapezoid is the sum of its side lengths:

P = (15 +3) +4 +15 +5 = 42 . . . . cm

Total area

SA = 2(66 cm²) + (42 cm)(6 cm) = 132 cm² +252 cm² = 384 cm²

The surface area of the composite figure is 384 cm².

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