Question

Pls pls pls pls help me answer this fast

Answer 1

Answer:

351

Step-by-step explanation:

The prism shown is a trapezoidal prism

The volume of a trapezoidal prism can be calculated by finding the area of the base and then multiplying that by the length of the prism

The base of a trapezoidal prism is a trapezoid

The area of a trapezoid can be calculated by using this formula

A = (a + b) / 2 * h

Where a and b = the base lengths and h = height

The base shown has base lengths ( a and b ) of 5cm and 8cm and the height (h) given is 6cm

To find the area we simply plug in these values into the formula

A = (a + b) / 2 * h

a = 5cm

b = 8cm

h = 6cm

* Plug in values *

A = (5 + 8) / 2 * 6

Add 5 and 8

A = 13/2 * 6

Divide 13 and 2

A = 6.5 * 6

Multiply 6.5 and 6

A = 39

So the area of the base is 39cm^2

Now to find the volume of the trapezoidal prism we simply multiply 39 by the length of the prism ( which would be 9)

So V = 39 * 9 = 351

And we are done!

Answer 2

Answer:

$351\:\mathrm{cm^3}$

Step-by-step explanation:

The area of this prism can be found by multiplying the area of the base by the height.

Since this only works if the two bases are the same, let's assign the congruent trapezoids on the front and back of the prism to be the trapezoid's bases.

The area of a trapezoid is equal to the average of its bases multiplied by its height. In this case, the height of each trapezoid is 6 and there are two bases 5 and 8. To find the average of a set of $n$ values, add up all the values of the set and divide by $n$. Therefore, the average of 5 and 8 is $\frac{5+8}{2}=\frac{13}{2}=6.5$ and the area of the trapezoid is:

$6\cdot 6.5=39\:\mathrm{cm^2}$

Now we multiply this by the prism's height (9 cm), to get our final answer:

$39\cdot 9=390-39=\boxed{351\:\mathrm{cm^3}}$