Question

The base of a right prism is a rhombus with diagonals of 6 and 8. If the altitude of the prism is 12, what is the total surface area of this prism?

Answer 1

total surface area is 432

Step-by-step explanation:

Given data

base = 6

diagonals = 8

altitude = 12

to find out

total surface area

solution

we know total surface area of prism is

total surface area = lateral surface area + 2base area ..............1

so

first we calculate base perimeter i.e = 2 length + 2 width

so perimeter = 2(8) + 2(6) = 25

and area = length * width = 8*6 = 48

so lateral surface area is perimeter * height i.e

lateral surface area = 28* 12

lateral surface area = 336

put this value in equation 1 we get

total surface area = lateral surface area + 2base area

total surface area = 336 + 2(48)

total surface area is 432

Answer 2

`A_(total) = 288 unit^2`

Step-by-step explanation:

Base of the right prism is a rhombus

So the base area of the prism is given as

`A = (1)/(2)d_1 d_2`

here we know that

`d_1 = 6`

`d_2 = 8`

`A = (1)/(2)(6)(8)`

`A = 24`

Area of its vertical side is given as

`A' = Length * height`

`A' = 5(12) = 60`

now total surface area is given

`A_(total) = 2A + 4A'`

`A_(total) = 2(24) + 4(60)`

`A_(total) = 288 unit^2`