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

Answer:

$A_{total} = 288 unit^2$

Explanation:

Base of the right prism is a rhombus

So the base area of the prism is given as

$A = \frac{1}{2}d_1 d_2$

here we know that

$d_1 = 6$

$d_2 = 8$

$A = \frac{1}{2}(6)(8)$

$A = 24$

Area of its vertical side is given as

$A' = Length \times height$

$A' = 5(12) = 60$

now total surface area is given

$A_{total} = 2A + 4A'$

$A_{total} = 2(24) + 4(60)$

$A_{total} = 288 unit^2$

Answer 2

Answer:

total surface area is 432

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