Question

Find the area.???????

Answer 1

well, we can check the units right off the grid.

so, below the x-axis, we have a rectangle, is a 10x3, so it has an area of 10*3.

above the x-axis we have a trapezoid, it has to parallel sides or bases, top is 6 units, bottom base is 10 units, and it has an altitude of 2.

we can just get the area of both, sum them up, and that's the area of the figure.

$\bf \textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} a,b=\stackrel{bases}{parallel~sides}\\ h=height \end{cases}\\\\ -------------------------------\\\\ \stackrel{rectangle}{(10\cdot 3)}~~+~~\stackrel{trapezoid}{\cfrac{h(a+b)}{2}}\implies \stackrel{rectangle}{(10\cdot 3)}~~+~~\stackrel{trapezoid}{\cfrac{2(6+10)}{2}} \\\\\\ 30+16\implies 46$

Answer 2

Use the distance formula on each side then find the area by using the formula for area of a rectangle on the bottom rectangle that points V U Z and Y make then use the formula for area of a trapezoid on the trapezoid that points V W X and Y make and add both of those answers together.