Question

Graph the points and find the area and perimeter of the shape. P(-4,-4), Q(-1,-1), R (5,-4)

Answer 1

Graphing

and we have:

base is the segment PR = 5 - ( -4 ) = 5 + 4 = 9 unitss

height is: 3 units

then area is

$A=\frac{bh}{2}=\frac{9\cdot3}{2}=\frac{27}{2}=13.5\text{ }$

for the perimeter, we use the distance between two points to find the required sides:

for segment QR

$\begin{gathered} QR=\sqrt[]{(x2-x1)^2+(y2-y1)^2} \\ QR=\sqrt[]{(5-(-1))^2+(-4-(-1))^2} \\ QR=\sqrt[]{(5+1)^2+(-4+1)^2} \\ QR=\sqrt[]{6^2+(-3)^2} \\ QR=\sqrt[]{36+9} \\ QR=\sqrt[]{45}=3\sqrt[]{5} \end{gathered}$

For segment PQ:

$\begin{gathered} PQ=\sqrt[]{(-1-(-4))^2+(-1-(-4))^2} \\ PQ=\sqrt[]{(-1+4)^2+(-1+4)^2} \\ PQ=\sqrt[]{3^2+3^2} \\ PQ=\sqrt[]{9+9} \\ PQ=\sqrt[]{18}=3\sqrt[]{2} \end{gathered}$

therefore the perimeter is:

$P=9+3\sqrt[]{5}+3\sqrt[]{2}=19.95$

answer: a = 13.5 sq units and p = 19.95 units