Question

find the perimeter and area of triangle lmk if each unit on the graph measures 1 centimeter. round your answer to the nearest
l(-1,6)
m(-4,2) k(2,2)
perimeter= cm
area= cm²

Explanation:

Step1: Calculate length of $MK$

$M(-4,2)$ and $K(2,2)$. Since $y$-coordinates are same, length $MK=\vert2 - (-4)\vert=6$ cm.

Step2: Calculate length of $LM$

Use distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For $L(-1,6)$ and $M(-4,2)$, $x_1=-1,y_1 = 6,x_2=-4,y_2 = 2$. Then $LM=\sqrt{(-4+1)^2+(2 - 6)^2}=\sqrt{(-3)^2+(-4)^2}=\sqrt{9 + 16}=\sqrt{25}=5$ cm.

Step3: Calculate length of $LK$

For $L(-1,6)$ and $K(2,2)$, $x_1=-1,y_1 = 6,x_2=2,y_2 = 2$. Then $LK=\sqrt{(2 + 1)^2+(2 - 6)^2}=\sqrt{3^2+(-4)^2}=\sqrt{9+16}=\sqrt{25}=5$ cm.

Step4: Calculate perimeter

Perimeter $P=LM + MK+LK=5 + 6+5 = 16$ cm.

Step5: Calculate area

Base $MK = 6$ cm, height from $L$ to $MK$ is the difference in $y$-coordinates of $L$ and the line $y = 2$, so height $h=6 - 2=4$ cm. Area $A=\frac{1}{2}\times base\times height=\frac{1}{2}\times6\times4 = 12$ $cm^2$.

Answer:

Perimeter = 16 cm
Area = 12 $cm^2$