Question

find the perimeter and area of this figure.
round your answer to the nearest hundredth.

Explanation:

Step1: Find the lengths of the sides

• Let the points be \(A(2,3)\), \(B(2,7)\), \(C(6,3)\)
• Length of \(AB\): Using the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\), for \(A(2,3)\) and \(B(2,7)\), \(d_{AB}=\sqrt{(2 - 2)^2+(7 - 3)^2}=\sqrt{0 + 16}=4\)
• Length of \(BC\): For \(B(2,7)\) and \(C(6,3)\), \(d_{BC}=\sqrt{(6 - 2)^2+(3 - 7)^2}=\sqrt{16 + 16}=\sqrt{32}\approx5.66\)
• Length of \(AC\): For \(A(2,3)\) and \(C(6,3)\), \(d_{AC}=\sqrt{(6 - 2)^2+(3 - 3)^2}=\sqrt{16+0}=4\)

Step2: Calculate the perimeter

Perimeter \(P = AB + BC+AC\)
\(P=4 + 5.66+4=13.66\)

Step3: Calculate the area

Using the formula for the area of a triangle \(A=\frac{1}{2}\times base\times height\)
Base \(AC = 4\), height \(AB = 4\)
\(A=\frac{1}{2}\times4\times4 = 8\)

Answer:

\(P = 13.66\) units, \(A=8\) units²