How do you find the lateral area and surface area of a right prism whose height is 10 ft and whose base is a rombus with diagonals 12 ft and

12sq root of 3 ( DON'T KNOW HOW TO PUT SQROOT 3 IN)

The area of a rhombus is 1/2 the product of the diagonals.

The top and bottom of your prism are rhombuses with areas of 60 sqrt3 ft^2, EACH.

The four rectangular sides of the prism each have areas of
(height)*[(a/2)^2 + (b/2)^2]
where a and b are the rhombus diagonal lengths. The term in brackets is the rhombus side length, and equals 12 feet in this case.

To find the lateral area and surface area of a right prism, you need to know the formula for each and apply it to the given measurements.

1. Lateral Area: The lateral area is the sum of the areas of all the faces of the prism, excluding the base(s).

In the case of a right prism, the lateral area can be found using the formula:

Lateral Area = Perimeter of the base × Height

To find the perimeter of the base, you need to know the length of the sides or the lengths of the diagonals.

For a rhombus, you can calculate the perimeter (P) based on the length of the diagonals (d1 and d2) using the formula:

P = 2 × (d1 + d2)

Given that the diagonals of the rhombus are 12 ft and 12√3 ft, you can substitute these values into the formula to find the perimeter of the rhombus.

2. Surface Area: The surface area of a right prism includes the base(s) in addition to the lateral area.

To find the surface area, you need to calculate the area of the base(s) and add it to the lateral area.

For a rhombus, the area (A) can be calculated using the formula:

A = (d1 × d2) / 2

Substitute the values of the diagonals to find the area of the base.

Then, add the area of the base to the lateral area to obtain the surface area.

Remember to use the proper units for the measurements (ft, in, m, etc.) to ensure consistent results in your calculations.