Question

find the perimeter and area of triangle lmk if each unit on the graph measures 1 centimeter. round your answer to the nearest centimeter, if necessary. equivalent experience_ma.912.gr.3.4 possible points: 6 perimeter= cm area= cm²

Explanation:

Step1: Calculate the lengths of the sides using the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$

For side $MK$ with $M(-4,2)$ and $K(2,2)$:
$d_{MK}=\sqrt{(2 - (-4))^2+(2 - 2)^2}=\sqrt{(2 + 4)^2+0^2}=\sqrt{6^2}=6$
For side $ML$ with $M(-4,2)$ and $L(-1,6)$:
$d_{ML}=\sqrt{(-1-(-4))^2+(6 - 2)^2}=\sqrt{(-1 + 4)^2+4^2}=\sqrt{3^2+4^2}=\sqrt{9 + 16}=\sqrt{25}=5$
For side $KL$ with $K(2,2)$ and $L(-1,6)$:
$d_{KL}=\sqrt{(-1 - 2)^2+(6 - 2)^2}=\sqrt{(-3)^2+4^2}=\sqrt{9+16}=\sqrt{25}=5$

Step2: Calculate the perimeter $P$

$P=d_{MK}+d_{ML}+d_{KL}=6 + 5+5=16$

Step3: Calculate the area $A$ using the formula for the area of a triangle with base and height

The base $MK = 6$ and the height (the perpendicular distance from $L$ to $MK$) is $4$.
$A=\frac{1}{2}\times base\times height=\frac{1}{2}\times6\times4 = 12$

Answer:

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