Question

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

Explanation:

Step1: Find the lengths of the sides

• Let the vertices be \(A(2,2)\), \(B(5,6)\), \(C(8,2)\)
• Use the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)
• \(AB=\sqrt{(5 - 2)^2+(6 - 2)^2}=\sqrt{9 + 16}=\sqrt{25}=5\)
• \(BC=\sqrt{(8 - 5)^2+(2 - 6)^2}=\sqrt{9 + 16}=\sqrt{25}=5\)
• \(AC=\sqrt{(8 - 2)^2+(2 - 2)^2}=\sqrt{36}=6\)

Step2: Calculate the perimeter \(P\)

• \(P=AB + BC+AC\)
• \(P = 5+5 + 6=16\)

Step3: Calculate the area \(A\)

• Base \(b = AC = 6\), height \(h=6 - 2=4\)
• Use the formula \(A=\frac{1}{2}\times b\times h\)
• \(A=\frac{1}{2}\times6\times4 = 12\)

Answer:

\(P = 16\) units, \(A=12\) units\(^2\)