Question

PLEASE HELPPPPPP!!!!!!!!!!​

Answer 1

Answers:

perimeter = 19.68324 units (approximate)

area = 16 square units

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Step-by-step explanation:

The distance from B to C is 8 units. Count out the spaces between the points, or you can subtract and apply absolute value.

We'll need the distance formula to find the segment lengths AB and AC.

I'll show the steps for AB

`A = (x_1,y_1) = (-2,3) \text{ and } B = (x_2, y_2) = (-4,-1)\\\\d = √((x_1 - x_2)^2 + (y_1 - y_2)^2)\\\\d = √((-2-(-4))^2 + (3-(-1))^2)\\\\d = √((-2+4)^2 + (3+1)^2)\\\\d = √((2)^2 + (4)^2)\\\\d = √(4 + 16)\\\\d = √(20)\\\\d = √(4*5)\\\\d = √(4)*√(5)\\\\d = 2√(5)\\\\d \approx 4.472136\\\\`

Segment AB is exactly
`2√(5)` units long. It approximates to about 4.472136 units.

Follow similar steps to determine that
`AC = 2√(13) \approx 7.211103\\\\`

Now that we know all three side lengths, we add them up to get the perimeter.

`AB+BC+AC = 2√(5)+8+2√(13) \approx 19.68324`

The perimeter is approximately 19.68324 units. Round this approximate value however your teacher instructs.

Or you could stick to the exact form involving those square roots. The downside to this is that it's hard to conceptualize how much fencing is needed to enclose this triangle.

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The area will be much easier to compute.

The base is BC = 8.

The height is 4 units because it's the vertical distance from point A to side BC. Take note the base and height are always perpendicular.

Then,

area = 0.5*base*height = 0.5*8*4 = 16 square units.