Question

find the perimeter and area of this figure.

round your answer to the nearest hundredth

Explanation:

Step1: Find the lengths of the sides

• The vertical side: The \(y -\)coordinates are \(y_1 = 3\) and \(y_2=7\). Using the distance formula for vertical line \(d=\vert y_2 - y_1\vert\), \(d_1=\vert7 - 3\vert=4\)
• The horizontal side: The \(x -\)coordinates are \(x_1 = 3\) and \(x_2 = 7\). Using the distance formula for horizontal line \(d=\vert x_2 - x_1\vert\), \(d_2=\vert7 - 3\vert = 4\)
• The hypotenuse: Using the Pythagorean theorem \(c=\sqrt{a^{2}+b^{2}}\), where \(a = 4\) and \(b = 4\). So \(c=\sqrt{4^{2}+4^{2}}=\sqrt{16 + 16}=\sqrt{32}\approx5.66\)

Step2: Calculate the perimeter

Perimeter \(P=a + b + c\). Substitute \(a = 4\), \(b = 4\), \(c\approx5.66\). \(P=4 + 4+5.66=13.66\)

Step3: Calculate the area

Area of a right - triangle \(A=\frac{1}{2}\times base\times height\). Here base \(a = 4\) and height \(b = 4\). \(A=\frac{1}{2}\times4\times4 = 8\)

Answer:

\(P = 13.66\) units, \(A=8\) units\(^{2}\)