Question

find the perimeter and area of this figure.
p = units
a = units²

Explanation:

Step1: Find the lengths of the sides

Assume the coordinates of the three points are \((2,9)\), \((8,9)\), \((8,1)\).
The length of the horizontal side: \(8 - 2=6\) (using \(x\)-coordinate difference).
The length of the vertical side: \(9 - 1 = 8\) (using \(y\)-coordinate difference).
For the slanted side, use the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here \((x_1,y_1)=(2,9)\), \((x_2,y_2)=(8,1)\), so \(d=\sqrt{(8 - 2)^2+(1 - 9)^2}=\sqrt{36 + 64}=\sqrt{100}=10\).

Step2: Calculate the perimeter

Perimeter \(P\) is the sum of all side - lengths. \(P=6 + 8+10=24\).

Step3: Calculate the area

The figure is a right - triangle. Area formula \(A=\frac{1}{2}\times base\times height\). Here base \(b = 6\), height \(h = 8\), so \(A=\frac{1}{2}\times6\times8 = 24\).

Answer:

\(P = 24\) units, \(A=24\) units²