Question

1. a shipping container in the shape of a rectangular prism is 60 feet long, 4.5 feet wide, and 14 feet tall. what is the volume of the shipping container?
2. what is the area of the polygon shown?
3. find the perimeter of a rectangle with a length of 5 units and a width of 3 units.
4. draw polygon abcdef in this coordinate - plane, given its vertices a(-2,-3), b(0,-3), c(0,1), d(3,1), e(3,3), f(-2,3).

Explanation:

Step1: Recall volume formula for rectangular prism

The volume $V$ of a rectangular prism is $V = l\times w\times h$, where $l$ is length, $w$ is width and $h$ is height. Given $l = 60$ feet, $w=4.5$ feet and $h = 14$ feet.
$V=60\times4.5\times14$

Step2: First multiply 60 and 4.5

$60\times4.5 = 270$

Step3: Then multiply the result by 14

$270\times14=3780$ cubic - feet

Step4: Recall area - decomposition for the polygon

The given polygon can be decomposed into a rectangle and a right - triangle.
The rectangle has length $l = 20$ mm and width $w = 14$ mm. The triangle has base $b=26 - 20=6$ mm and height $h = 14$ mm.
The area of the rectangle $A_{r}=l\times w=20\times14 = 280$ $mm^{2}$
The area of the triangle $A_{t}=\frac{1}{2}\times b\times h=\frac{1}{2}\times6\times14 = 42$ $mm^{2}$
The area of the polygon $A = A_{r}+A_{t}=280 + 42=322$ $mm^{2}$

Step5: Recall perimeter formula for rectangle

The perimeter $P$ of a rectangle is $P=2(l + w)$. Given $l = 5$ units and $w = 3$ units.
$P=2(5 + 3)=2\times8 = 16$ units

Answer:

1. Volume of the shipping container: 3780 cubic feet
2. Area of the polygon: 322 square millimeters
3. Perimeter of the rectangle: 16 units
4. For drawing polygon ABCDEF:

• Plot point A at $(-2,-3)$
• Plot point B at $(0,-3)$
• Plot point C at $(0,1)$
• Plot point D at $(3,1)$
• Plot point E at $(3,3)$
• Plot point F at $(-2,3)$
• Connect the points in order A - B - C - D - E - F - A.