Question

find the perimeter and area of this figure
p = ? units
a = units²
round your answer to the nearest hundredth

Explanation:

Step1: Find the lengths of the sides

Let the points be \(A(2,2)\), \(B(5,9)\), \(C(9,2)\)
Use the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)
For \(AB\): \(d_{AB}=\sqrt{(5 - 2)^2+(9 - 2)^2}=\sqrt{9 + 49}=\sqrt{58}\approx7.62\)
For \(BC\): \(d_{BC}=\sqrt{(9 - 5)^2+(2 - 9)^2}=\sqrt{16 + 49}=\sqrt{65}\approx8.06\)
For \(AC\): \(d_{AC}=\sqrt{(9 - 2)^2+(2 - 2)^2}=\sqrt{49}=7\)

Step2: Calculate the perimeter \(P\)

\(P=d_{AB}+d_{BC}+d_{AC}\approx7.62 + 8.06+7 = 22.68\)

Step3: Calculate the area \(A\)

Base \(b = AC = 7\), height \(h\) is the vertical distance from \(B\) to \(AC\), \(h=9 - 2=7\)
Use the formula \(A=\frac{1}{2}\times b\times h\)
\(A=\frac{1}{2}\times7\times7 = 24.5\)

Answer:

\(P = 22.68\) units, \(A = 24.50\) units²