Answer:
Perimeter = 96.3 in
Area = 548.1 in²
Height = 17 in
Step-by-step explanation:
Perimeter
The perimeter of the trapezoidal base is the sum of the lengths of all its sides. Therefore:
[tex]\sf Perimeter = 19 + 20.3 + 35 + 22\\\\Perimeter = 96.3 \;in[/tex]
So, the perimeter of the trapezoidal base is 96.3 inches.
[tex]\dotfill[/tex]
Area
To find the area of the trapezoidal base, we can use the formula for the area of a trapezoid:
[tex]\boxed{\begin{array}{l}\underline{\textsf{Area of a trapezoid}}\\\\A=\dfrac{1}{2}(b_1+b_2)h\\\\\textsf{where:}\\ \phantom{ww}\bullet\;\textsf{$A$ is the area.}\\ \phantom{ww}\bullet\;\textsf{$b_1$ and $b_2$ are the parallel sides (bases).}\\\phantom{ww}\bullet\;\textsf{$h$ is the height (perpendicular to the bases).}\end{array}}[/tex]
In this case, the two bases measure 19 in and 35 in, and the height is 20.3 in. Therefore:
[tex]\sf Area=\dfrac{1}{2}(19+35)\cdot 20.3\\\\\\Area=\dfrac{1}{2}(54)\cdot 20.3\\\\\\Area=27\cdot 20.3\\\\\\Area=548.1\; in^2[/tex]
So, the area of the trapezoidal base is 548.1 square inches.
[tex]\dotfill[/tex]
Height
The bases of a prism are the two parallel polygonal faces that define the shape of the prism. These bases are congruent and lie opposite each other. The height of a prism is the perpendicular distance between these two parallel bases.
In this case, the bases are trapezoids. So, the height of the prism is the perpendicular distance between the two trapezoid bases. Therefore, the height of the prism is 17 inches.
