Question

A prism of height 12" has a rhombus with diagonals 6" and 8" for a base. Find the volume. 240 cu. in. 288 cu. in. 576 cu. in.

Answer 1

its not 576 because i got it wrong 

Answer 2

Answer:

Option 2nd is correct

volume of prism is, 288 cu. in.

Step-by-step explanation:

Volume of prism(V) is given by:

$V = B \cdot h$               .....[1]

where,

B is the Base area

h is the height of the prism.

Area of rhombus(A) is given by:

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

where,

$d_1, d_2$ are the diagonals of the rhombus.

As per the statement:

A prism of height 12" has a rhombus with diagonals 6" and 8" for a base.

⇒$d_1 = 6"$, $d_2= 8"$ and h = 12"

Find the base area i.,e Area of rhombus.

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

Simplify:

$B = 24$ square inches.

Substitute the given values in [1] we have;

$V = 24 \cdot 12 = 288$ cubic inches.

Therefore, the volume of prism is, 288 cu. in.