The base of a right prism is a rhombus whose sides are 20cm and the shorter diagonal is 24in..find the area pls.

The diagonals of a rhombus bisect each other at right angles.

You should see 4 identical right-angled triangles
let the missing side in each of those triangles be x

x^2 + 12^2 = 20^2
x = 16
So the longer diagonal is 32

Area of rhomus = (1/2)(product of diagonals)
= ...

where did u get the 12?because the sides are centimeter and the other diagonal is inches?

Didn't notice that.

Weird that they would mix units like that.
Anyway,
1 inch = 2.54 cm

As I said, the diameters right-bisect each other, so what is 1/2 of 24 ?
So change the 12 inches to cm
= 12(2.54) cm
= 30.48 cm
Now everything is in the same units.

To find the area of the base of a right prism, we need to know the formula for the area of the given shape. In this case, since the base is a rhombus, we can use the formula for finding the area of a rhombus.

The formula for the area of a rhombus is:
Area = (diagonal1 * diagonal2) / 2

In the given problem, we are told that the sides of the rhombus are 20 cm and the shorter diagonal is 24 in. However, to calculate the area accurately, we need to convert the measurements to the same unit. Let's convert the shorter diagonal from inches to centimeters.

1 inch = 2.54 cm
So, 24 inches = 24 * 2.54 cm = 60.96 cm

Now we can use the formula to find the area of the rhombus:
Area = (diagonal1 * diagonal2) / 2
= (20 cm * 60.96 cm) / 2
= (1219.2 cm^2) / 2
= 609.6 cm^2

Thus, the area of the base of the right prism is 609.6 square centimeters (cm^2).