Question

90 points please help real answers !!!
Type the correct answer in each box. If necessary, round your answer(s) to the nearest hundredth.
The vertices of ∆ABC are A(-2, 2), B(6, 2), and C(0, 8). The perimeter of ∆ABC is
(blank)units, and its area is (blank)
square units.

Answer 1

Find the length of each side using the distance formula:, then add all three side length for the perimeter.

Area is found by multiplying the base by the height by 1/2.

See attached picture for the answer:

Answer 2

The perimeter of ∆ABC is 22.8 units and  its area 23.84 unit²

Using the distance formula,

d = √(x₂ - x₁)² + (y₂ - y₁)²

The sides can be found as follows;

A(-2, 2), B(6, 2), and C(0, 8)

AB = √(6 + 2)² + (2 - 2)² = √64 = 8 units

AC = √(0 + 2)² + (8 - 2)² = √4 + 36 = √40 = 6.3 units

BC = √(0 - 6)² + (8 - 2)² = √36 + 36 = √72 = 8.5 units

Therefore,

perimeter = 8 + 6.3 + 8.5 = 22.8 units

Area = √s(s - a)(s - b)(s - c)

s = a + b + c / 2

s = 8.5 + 6.3 + 8 / 2 = 22.8 / 2 = 11.4

Area = √11.4(11.4 - 8.5)(11.4 - 6.3)(11.4 - 8)

Area = 23.84 unit²

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