type the correct answer in each box. if necessary, round your answer(s) to the nearest hundredth. the…

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.

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.

Answer

Explanation:

Step1: Calculate length of AB

Points A(-2,2) and B(6,2). Since y-coordinates are same, distance AB = |6 - (-2)| = 8.

Step2: Calculate length of AC

Using distance formula: (d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}). For A(-2,2) and C(0,8): (AC = \sqrt{(0 - (-2))^2 + (8 - 2)^2} = \sqrt{4 + 36} = \sqrt{40} \approx 6.32).

Step3: Calculate length of BC

For B(6,2) and C(0,8): (BC = \sqrt{(0 - 6)^2 + (8 - 2)^2} = \sqrt{36 + 36} = \sqrt{72} \approx 8.49).

Step4: Calculate perimeter

Perimeter = AB + AC + BC = 8 + 6.32 + 8.49 ≈ 22.81.

Step5: Calculate area

Base AB = 8, height is vertical distance from C to AB (since AB is horizontal). y-coordinate of AB is 2, y-coordinate of C is 8, so height = 8 - 2 = 6. Area = (\frac{1}{2} \times 8 \times 6 = 24).

Answer:

Perimeter: (\boldsymbol{22.81}), Area: (\boldsymbol{24})