Question

type the correct answer in each box. if necessary, round your answer(s) to the nearest hundredth. the vertices of δabc are a(-2, 2), b(6, 2), and c(0, 8). the perimeter of δabc is units, and its area is square units.

Explanation:

Step1: Calculate length of AB

Points A(-2,2) and B(6,2) share the same y-coordinate, so subtract x-values:
$AB = |6 - (-2)| = 8$

Step2: Calculate length of BC

Use distance formula $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ for B(6,2) and C(0,8):
$BC = \sqrt{(0-6)^2+(8-2)^2} = \sqrt{36+36} = \sqrt{72} \approx 8.49$

Step3: Calculate length of AC

Use distance formula for A(-2,2) and C(0,8):
$AC = \sqrt{(0-(-2))^2+(8-2)^2} = \sqrt{4+36} = \sqrt{40} \approx 6.32$

Step4: Calculate perimeter

Sum the three side lengths:
$Perimeter = 8 + 8.49 + 6.32 = 22.81$

Step5: Calculate area using base-height

AB is the base ($=8$), height is vertical distance from C to AB:
Height = $8 - 2 = 6$
$Area = \frac{1}{2} \times base \times height = \frac{1}{2} \times 8 \times 6$

Answer:

Perimeter: $22.81$
Area: $24$