Find the lateral surface area and the total surface area.

LA = 96

SA = 108

Step-by-step explanation:

The lateral surface area is the area of the sides (not including the bases).  For a triangular prism, the bases are the triangles.

The sides consist of three rectangles.  The vertical rectangle is 3 by 8 units.  The horizontal rectangle is 4 by 8 units.

The slanted rectangle has a length of 8 units, but we don't know the width.  To find that, we use Pythagorean theorem to find the hypotenuse of the triangles.

c² = a² + b²

c² = 3² + 4²

c = 5

So the lateral surface area is:

LA = (3)(8) + (4)(8) + (5)(8)

LA = 96

The total surface area is the lateral surface area plus the area of the bases.

SA = 96 + ½(3)(4) + ½(3)(4)

SA = 108

Heya,

This triangle is made up of 3 rectangles and 2 triangles. We don't know what the width of the slanted triangle is, so, we can use the Pythagorean theorem to solve for the width (hypotenuse).

a² + b² = c²

3² + 4² = c²

9 + 16 = c²

25 = c²

√25 = √c²

5 = c

Now, that we know what the width of the slanted triangle is, we can solve for the total surface area.

= (2(3)(4))/2 + (8)(3) + (8)(4) + (8)(5)

= 12 + 24 + 32 + 40

= 108 units is the total surface area.

The base are the two triangles to each side of the triangle. So, just subtract.

108 - 12 = 96 units is the lateral surface area.

Best of Luck!

the mistake in the pattern is that :

b. the decimal point was moved one too many place values each time

the correct pattern could be made by :

b. moving the decimal point to the right the same numbers of place values as the exponents