Question

What is the perimeter of the composite figure? Round to the nearest tenth

Answer 1

Answer:

123.8 units

Step-by-step explanation:

The vertices of the polygon has been labelled ABCDEF, as shown in the diagram attached below.

Perimeter of the Polygon = $\overline{AB} + \overline{BC} + \overline{CD} + \overline{DE} + \overline{EF} + \overline{FA}$

$\overline{AB}$ = |-12 - 24| = |-36| = 36 units

$\overline{BC}$: calculate the distance between B(24, 16) and C(15, 3) using the distance formula.

$\overline{BC} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

$\overline{BC} = \sqrt{(24 - 15)^2 + (16 - 3)^2}$

$\overline{BC} = \sqrt{(9)^2 + (13)^2}$

$\overline{BC} = \sqrt{81 + 169} = \sqrt{250}$

$\overline{BC} = 15.8 units$

$\overline{CD}$ = |6 - 15| = |-9| = 9 units

$\overline{DE}$ = |3 -(-12)| = |-15| = 15 units

$\overline{EF}$ = |-12 - 6| = |-18| = 18 units

$\overline{FA}$ = |18 -(-12)| = 30 units

Perimeter = 36 + 15.8 + 9 + 15 + 18 + 30 = 123.8 units