Question

find the area of this trpaezoid really need help on this one. answers A). 4sqrt3 B)12.0 C)8sqrt2 D)16sqrt2

Answer 1

check the picture below.

so, then using the pythagorean theorem, we can get "b", namely the height of the trapezoid.


`\bf \textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} a,b=\stackrel{bases}{parallel~sides}\\ h=height\\ ---------\\ a=3\\ b=\stackrel{1+4}{5}\\ h=√(8) \end{cases}\implies A=\cfrac{√(8)(3+5)}{2} \\\\\\ A=\cfrac{8√(8)}{2}~~ \begin{cases} 8=2\cdot 2\cdot 2\\ \qquad 2^2\cdot 2 \end{cases}\implies A=\cfrac{8√(2^2\cdot 2)}{2}\implies A=\cfrac{8\cdot 2√(2)}{2} \\\\\\ A=\cfrac{16√(2)}{2}\implies A=8√(2)`