Question

Find the lateral area for the prism.
L.A. =

Answer 1

The correct answer is 80 + 16√13 feet²

Explanation:

Like we can see in the plot, the prism has three rectangular sides, that are its lateral area. For calculating the area, we need to add up the three sides, this way:

Height of the prism (h) = 8 ' or 8 feet

Area of the first side = 8 * 4 = 32 feet²

Area of the third side = 8 * 6 = 48 feet²

Area of the third side = 8 * Hypotenuse of the triangle

Hypotenuse of the triangle² = 4² + 6² = 52

Hypotenuse of the triangle =√52 = √13 * 4 = 2√13 feet

Area of the third side = 8 * 2√13 feet = 16√13 feet²

Area lateral of the prism = 32 + 48 + 16√13 = 80 + 16√13 feet²

Answer 2

L.A. = 80 + 16√13

Explanation:

the lateral area is the area of the vertical faces.

So, for the given prism = The sum of the area of the vertical rectangles.

= height * perimeter of the right triangle.

The hypotenuse of the right triangle =
`√(6^2+4^2) = √(36+16) =√(52) =√(4*13) =2√(13)`

So, the sides of the triangle are 4 , 6 and 2√13

The perimeter of the right triangle = 4 + 6 + 2√13 = 10 + 2√13

Height = 8

The lateral area for the prism = 8 * ( 10 + 2√13 ) = 80 + 16√13