Question

What is the area of triangle ABC?

3 square units
7 square units
11 square units
15 square units

Answer 1

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

`A=√(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:

`A (1,1)\\B: (4,0)\\C: (3,5)\\`

`AB=\sqrt {(x2-x1) ^ 2+(y2-y1) ^ 2}\\AB =\sqrt {(4-1) ^ 2+(0-1) ^ 2}\\AB=\sqrt {3 ^ 2+(- 1) ^ 2}\\AB =\sqrt {10}\\AB = 3.16`

We found BC:

`BC =\sqrt {(x2-x1) ^ 2 + (y2-y1) ^ 2}\\BC =\sqrt {(3-4) ^ 2 + (5-0) ^ 2}\\BC =\sqrt {(- 1) ^ 2 + 5 ^ 2}\\BC = \sqrt {26}\\BC = 5.10`

We found CA:

`CA=\sqrt {(x2-x1) ^ 2 + (y2-y1) ^ 2}\\CA=\sqrt {(1-3) ^ 2 + (1-5) ^ 2}\\CA=\sqrt {(- 2) ^ 2 + (- 4) ^ 2}\\CA=\sqrt {4 + 16}\\CA = \sqrt {20}\\CA = 4.47`

So, half of the perimeter is:

`s = \frac{3.16 + 5.10 + 4.47} {2} = 6.365`

Thus, the area is:

`A=\sqrt {6.365 (6.365-3.16) (6.365-5.10) (6.365-4.47)}\\A=\sqrt {6,365 (3,205) (1,265) (1,895)}\\A = \sqrt {48.90}\\A = 6.99`

Rounding we have that the area is 7 square units

Answer:

Option B

Answer 2

7 square units.

Explanation:

We could use put a rectangle around the shape box. That would leave you with 3 other triangles and subtract that from the rectangles to get the primary triangle. so the 3 triangle areas are 2.5, 1.5, and 4. if you add those u get 8. The rectangle is 15 sq units so 15-8 is 7.