Question

find the perimeter and area of this figure
p =? units
a = units

Explanation:

Step1: Find the lengths of the sides

Let the points be \(A(3,7)\), \(B(3,3)\), \(C(7,3)\).
The length of \(AB\): Using the distance formula for vertical line \(d=\vert y_2 - y_1\vert\), \(AB=\vert7 - 3\vert = 4\) units.
The length of \(BC\): Using the distance formula for horizontal line \(d=\vert x_2 - x_1\vert\), \(BC=\vert7 - 3\vert = 4\) units.
The length of \(AC\): Using the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\), \(AC=\sqrt{(7 - 3)^2+(3 - 7)^2}=\sqrt{16 + 16}=\sqrt{32}\approx5.66\) units.

Step2: Calculate the perimeter \(P\)

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

Step3: Calculate the area \(A\)

Using the formula for the area of a right - triangle \(A=\frac{1}{2}\times base\times height\). Here, base \(BC = 4\) and height \(AB = 4\).
\(A=\frac{1}{2}\times4\times4=8\) units².

Answer:

\(P = 13.66\) units, \(A = 8\) units²