Question

find the perimeter and area of the figure if each unit on the graph measures 1 centimeter. round answers to the nearest tenth, if necessary

Explanation:

Step1: Find the lengths of the sides using the distance formula

The distance formula is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
Let the points be \(A(2,12)\), \(B(10,2)\), \(C(2,2)\).
For \(AB\): \(x_1 = 2,y_1 = 12,x_2 = 10,y_2 = 2\)
\(AB=\sqrt{(10 - 2)^2+(2 - 12)^2}=\sqrt{64 + 100}=\sqrt{164}\approx12.8\)
For \(BC\): \(x_1 = 10,y_1 = 2,x_2 = 2,y_2 = 2\)
\(BC=\sqrt{(2 - 10)^2+(2 - 2)^2}=\sqrt{64+0}=8\)
For \(AC\): \(x_1 = 2,y_1 = 12,x_2 = 2,y_2 = 2\)
\(AC=\sqrt{(2 - 2)^2+(2 - 12)^2}=\sqrt{0 + 100}=10\)

Step2: Calculate the perimeter

Perimeter \(P=AB + BC+AC\)
\(P\approx12.8+8 + 10=30.8\)

Step3: Calculate the area

Since \(BC\) is parallel to the \(x -\)axis and \(AC\) is parallel to the \(y -\)axis, the base \(b = BC = 8\) and height \(h=AC = 10\)
The area formula for a triangle is \(A=\frac{1}{2}bh\)
\(A=\frac{1}{2}\times8\times10 = 40\)

Answer:

Perimeter: \(30.8\) centimeters, Area: \(40\) square centimeters