Question

Find the volume of each prism. Round your answers to the nearest tenth, if necessary. Do not include units (i.e. ft, in, cm, etc.). (FR)

Answer 1

Step-by-step explanation:

Given;

We are given the picture of an isosceles trapezoidal prism.

The dimensions are as follows;

`\begin{gathered} Top\text{ }base=4 \\ Bottom\text{ }base=9 \\ Vertical\text{ }height=4.3 \\ Height\text{ }between\text{ }bases=6 \end{gathered}`

Required;

We are required to find the volume of this trapezoidal prism.

Step-by-step solution;

The area of the base of a trapezium is given as;

`Area=(1)/(2)(a+b)* h`

For the trapezium given and the values provided, we now have;

`\begin{gathered} a=top\text{ }base \\ b=bottom\text{ }base \\ h=height \\ Therefore: \\ Area=(1)/(2)(4+9)*4.3 \\ Area=(1)/(2)(13)*4.3 \\ Area=6.5*4.3 \\ Area=27.95 \end{gathered}`

The volume is now given as the base area multiplied by the length between both bases and we now have;

`\begin{gathered} Volume=Area* height\text{ }between\text{ }trapezoid\text{ }ends \\ Volume=27.95*6 \\ Volume=167.7 \end{gathered}`

ANSWER:

The volume of the prism is 167.7