Question

The corners of a triangle are (2,1) and (3,4) and (0,5). What is its area? Add a corner at (-1,0) to make a lopsided region (four sides). Find the area.

A. 3 square units

B. 4 square units

C. 5 square units

D. 6 square units

Answer 1

The area of the triangle is 5 square units.

Step-by-step explanation:

To find the area of a triangle, you can use the formula:

Area = 1/2 * base * height

For the given triangle with corners (2,1), (3,4), and (0,5), we can find the base and height by using the distance formula between the two points. The distance between (2,1) and (3,4) is the base, and the distance between (3,4) and (0,5) is the height.

After calculating the base and height, we can substitute the values into the formula to find the area of the triangle:

Area = 1/2 * base * height

Area = 1/2 * (distance between (2,1) and (3,4)) * (distance between (3,4) and (0,5))

Area = 1/2 * sqrt ((3-2) ^2 + (4-1) ^2) * sqrt ((0-3) ^2 + (5-4) ^2)

Area = 1/2 * sqrt (1 + 9) * sqrt (9 + 1)

Area = 1/2 * sqrt (10) * sqrt (10)

Area = 1/2 * 10

Area = 5 square units