Question

11th grade geometry:

Answer 1

Answer:

The perimeter is 72 units and the area is 149 square units.

Step-by-step explanation:

$\triangle SBA$ has coordinates $S(15,-8),B(-2,21)$ and $A(0,0)$

Using the distance formula.........

Length of side $SB = \sqrt{(15+2)^2+(-8-21)^2}= \sqrt{17^2+(-29)^2}= \sqrt{1130}$

Length of side $BA= \sqrt{(-2)^2+(21)^2}= \sqrt{445}$

Length of side $AS =\sqrt{(15)^2+(-8)^2}=\sqrt{289}=17$

So, the perimeter of the triangle will be:  $(SB+BA+AS)= \sqrt{1130}+ \sqrt{445}+17 =71.71... \approx 72$ units.   (Rounded to the nearest unit)

The height of the triangle for the corresponding base $SB$ is 8.89 units.

Formula for the Area of triangle,  $A= \frac{1}{2}(base\times height)$

So, the area of the $\triangle SBA$ will be:  $\frac{1}{2}(\sqrt{1130}\times 8.89)= 149.42... \approx 149$ square units.   (Rounded to the nearest unit)