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 \(A(2,3)\), \(B(2,7)\), \(C(7,3)\).
The length of \(AB\): Using the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\), for \(A(2,3)\) and \(B(2,7)\), \(d_{AB}=\sqrt{(2 - 2)^2+(7 - 3)^2}=\sqrt{0 + 16}=4\).
The length of \(AC\): For \(A(2,3)\) and \(C(7,3)\), \(d_{AC}=\sqrt{(7 - 2)^2+(3 - 3)^2}=\sqrt{25+0}=5\).
The length of \(BC\): For \(B(2,7)\) and \(C(7,3)\), \(d_{BC}=\sqrt{(7 - 2)^2+(3 - 7)^2}=\sqrt{25 + 16}=\sqrt{41}\approx6.40\).

Step2: Calculate the perimeter \(P\)

\(P=AB + AC+BC\).
\(P = 4+5 + 6.40=15.40\).

Step3: Calculate the area \(A\)

Using the formula for the area of a triangle \(A=\frac{1}{2}\times base\times height\). Here, base \(AC = 5\) and height \(AB=4\).
\(A=\frac{1}{2}\times5\times4=10\).

Answer:

\(P = 15.40\) units, \(A = 10.00\) units²