Question

The coordinate plane below shows a triangular region at sea between three islands. Each unit on the coordinate plane represents 10 miles.



What are the area and perimeter of the triangular region? Round all answers to the nearest whole number.

Type your answers in the boxes below.

The area is
​

ñ
square miles.
The perimeter is approximately
​

ñ
miles.

Answer 1

I can do that, but I don't see the picture. Could you either upload the coordinate plane image or type the coordinates of the three triangle vertices?

While you get that to me, here are the formulas I'll use (and how the 10-mile scale is applied):

- If the triangle vertices are (x1,y1), (x2,y2), (x3,y3) in grid units:

- Area in unit^2 (shoelace):
A_units = 0.5 * | x1(y2−y3) + x2(y3−y1) + x3(y1−y2) |

- Area in square miles:
A_mi2 = A_units * (10 miles)^2 = A_units * 100

- Side lengths in miles (distance formula, then scale by 10):
d12 = 10 * sqrt[(x1−x2)^2 + (y1−y2)^2]
d23 = 10 * sqrt[(x2−x3)^2 + (y2−y3)^2]
d31 = 10 * sqrt[(x3−x1)^2 + (y3−y1)^2]

- Perimeter in miles:
P_mi = d12 + d23 + d31

I will round the final area and perimeter to the nearest whole number. Send the coordinates (or the image) and I’ll compute the answers.