Question

i do! example plot each group of points on the coordinate grid and label with the corresponding letter. then, connect the points in order and find the perimeter and area of the polygon. round to the nearest hundredth if needed. a(1,1) b(7,1) c(7,7)

Explanation:

Step1: Identify the polygon

The points A(1,1), B(7,1), C(7,7) form a right - angled triangle.

Step2: Calculate the lengths of the sides using the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$

For side AB: $x_1 = 1,y_1 = 1,x_2 = 7,y_2 = 1$. Then $AB=\sqrt{(7 - 1)^2+(1 - 1)^2}=\sqrt{6^2+0^2}=6$.
For side BC: $x_1 = 7,y_1 = 1,x_2 = 7,y_2 = 7$. Then $BC=\sqrt{(7 - 7)^2+(7 - 1)^2}=\sqrt{0^2+6^2}=6$.
For side AC: $x_1 = 1,y_1 = 1,x_2 = 7,y_2 = 7$. Then $AC=\sqrt{(7 - 1)^2+(7 - 1)^2}=\sqrt{6^2+6^2}=\sqrt{36 + 36}=\sqrt{72}=6\sqrt{2}\approx8.49$.

Step3: Calculate the perimeter

Perimeter $P=AB + BC+AC=6 + 6+6\sqrt{2}\approx6 + 6+8.49 = 20.49$.

Step4: Calculate the area

Area $A=\frac{1}{2}\times base\times height$. Here, base = AB = 6 and height = BC = 6. So $A=\frac{1}{2}\times6\times6 = 18$.

Answer:

Perimeter: 20.49, Area: 18