Question

What is the area of triangle QRS?

Answer 1

For this case we have to find the area through Heron's formula:

$A = \sqrt{s (s-a) (s-b) (s-c)}$

Where:

s: It's half the perimeter of the triangle

a, b, c are the sides.

We can find the sides by equating the distance between two points:

$S: (- 2, -2)\\Q: (- 1,2)\\R: (1, -4)$

$SQ=\sqrt {(x2-x1) ^ 2+(y2-y1) ^ 2}\\SQ=\sqrt {(- 1 + 2) ^ 2+ (2 + 2) ^ 2}\\SQ=\sqrt {1 ^ 2 +(4) ^2}\\SQ=\sqrt {17}\\SQ=4.12$

We found QR:

$QR = \sqrt {(x2-x1) ^ 2 + (y2-y1) ^ 2}\\QR = \sqrt {(1 + 1) ^ 2 + (- 4-2) ^ 2}\\QR = \sqrt {(2) ^ 2 + (- 6) ^ 2}\\QR = \sqrt {40}\\QR = 6.33$

We found RS:

$RS=\sqrt{(x2-x1)^2+(y2-y1)^2}\\RS=\sqrt{(1 + 2)^2+(- 4 + 2)^2}\\RS=\sqrt{(3)^2+(- 2)^2}\\RS=\sqrt{9+4}\\RS=\sqrt {13}\\RS=3.60$

So, half of the perimeter is:

$s = \frac {4.12 + 6.33 + 3.61} {2} = 7.03$

Thus, the area is:

$A = \sqrt{7.03 (7.03-4.12) (7.03-6.33) (7.03-3.61)}\\A = \sqrt{7.03 (2.91) (0.7) (3.42)}\\A = \sqrt {48.97}\\A = 6,997$

Rounding we have that the area is 7 square units

Answer:

Option A

Answer 2

Answer:

If you are looking for an explanation..

Step-by-step explanation:

It is 7 because if you use the box it out method, you would get 4 triangles and 1 primary one to look for. the other 3 would be 3,2, and 6. Added it would be 11 and subtracted from the rectangles, 18 you would get 7.