Question

find the perimeter and area of the figure if each unit on the graph measures 1 centimeter. round answers to the nearest tenth, if necessary.
perimeter:
cm
area:
cm²

Explanation:

Step1: Find lengths of sides

• \( AB \): Distance between \( A(0,9) \) and \( B(4,9) \). Since \( y \)-coordinates are same, \( AB = |4 - 0| = 4 \) cm.
• \( AC \): Distance between \( A(0,9) \) and \( C(0,1) \). Since \( x \)-coordinates are same, \( AC = |9 - 1| = 8 \) cm.
• \( BC \): Distance between \( B(4,9) \) and \( C(0,1) \). Use distance formula \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \). So \( BC = \sqrt{(4 - 0)^2 + (9 - 1)^2} = \sqrt{16 + 64} = \sqrt{80} \approx 8.94 \) cm.

Step2: Calculate perimeter

Perimeter \( = AB + AC + BC = 4 + 8 + 8.94 \approx 20.94 \) cm (rounded to nearest tenth).

Step3: Calculate area

The figure is a triangle with base \( AB = 4 \) cm and height \( AC = 8 \) cm (or height from \( C \) to \( AB \) is 8 cm). Area of triangle \( = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 4 \times 8 = 16 \) \( \text{cm}^2 \).

Answer:

Perimeter: \( \approx 20.9 \) cm (or 20.94 cm), Area: \( 16 \) \( \text{cm}^2 \)