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.
perimeter: cm
area: cm²

Explanation:

Step1: Calculate the lengths of the sides

• \(AC\): Since \(A(0,9)\) and \(C(0,1)\), using the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\), here \(x_1 = x_2=0\), so \(AC=\vert9 - 1\vert=8\) cm.
• \(AB\): Since \(A(0,9)\) and \(B(4,9)\), \(x_1 = 0,y_1 = 9,x_2 = 4,y_2 = 9\), then \(AB=\vert4 - 0\vert=4\) cm.
• \(BC\): Using the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\) with \(B(4,9)\) and \(C(0,1)\), \(d=\sqrt{(4 - 0)^2+(9 - 1)^2}=\sqrt{16 + 64}=\sqrt{80}=4\sqrt{5}\approx8.9\) cm.

Step2: Calculate the perimeter

Perimeter \(P=AB + AC+BC\). Substitute the values: \(P = 4+8 + 8.9=20.9\) cm.

Step3: Calculate the area

The formula for the area of a triangle is \(A=\frac{1}{2}\times base\times height\). Here, base \(AC = 8\) cm and height \(AB = 4\) cm. So \(A=\frac{1}{2}\times8\times4=16\) \(cm^{2}\).

Answer:

perimeter: \(20.9\) cm
area: \(16\) \(cm^{2}\)