Question

Brainliest question please help me answer my question please

Answer 1

Answer:

Step-by-step explanation:

The area for a trapezoid is

$A=\frac{1}{2}h(b_{1}+b_{2})$

h is the length of ST, one of the bases is the length of MK, and the other base is the length of AS.  First we'll find h:

The coordinates for S are (0, -2) and T are (1, 2). Using the distance formula:

$d=\sqrt{(1-0)^2+(2-(-2))^2$ and

$d=\sqrt{17}$.  So h = √17

Now for the length of MK. The coordinates for M are (-7, 4) and for K (5, 1). Using the distance formula again:

$d=\sqrt{(-7-5)^2+(4-1)^2}$ and

$d=\sqrt{(-12)^2+(3)^2}$ so

$d=\sqrt{153}$ which simplifies to

$d=3\sqrt{17}$. So MK = 3√17.

Now for the length of AS. The coordinates for A: (-4, -1) and for S: (0, -2). Using the distance formula one more time:

$d=\sqrt{(-4-0)^2+(-1-(-2))^2}$ and

$d=\sqrt{(-4)^2+(1)^2}$ and

$d=\sqrt{17}$. So AS = √17.

Now we can fill in our area formula:

$A=\frac{1}{2}(\sqrt{17})(3\sqrt{17}+\sqrt{17})$

Simplifying a bit:

$A=\frac{1}{2}(\sqrt{17})(4\sqrt{17})$ and simplifying a bit more:

$A=\frac{4*17}{2}$ and

A = 34