Question

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

Explanation:

Step1: Label the vertices

Let the vertices be \( A(2,2) \), \( B(7,2) \), \( C(5,6) \).

Step2: Calculate side lengths

Use the distance formula \( d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} \).

• \( AB=\sqrt{(7 - 2)^2+(2 - 2)^2}=\sqrt{25}=5 \)
• \( BC=\sqrt{(5 - 7)^2+(6 - 2)^2}=\sqrt{4 + 16}=\sqrt{20}=2\sqrt{5} \)
• \( AC=\sqrt{(5 - 2)^2+(6 - 2)^2}=\sqrt{9 + 16}=\sqrt{25}=5 \)

Step3: Calculate perimeter \( P \)

\( P=AB + BC+AC=5 + 2\sqrt{5}+5=10 + 2\sqrt{5}\approx10 + 4.47=14.47 \)

Step4: Calculate area \( A \)

Base \( b = AB = 5 \), height \( h=6 - 2 = 4 \).
Using the formula \( A=\frac{1}{2}\times b\times h \), \( A=\frac{1}{2}\times5\times4 = 10 \)

Answer:

\( P\approx14.47 \) units, \( A = 10 \) units\( ^2 \)